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Deep factorisation of the stable processFeb 25 2015Aug 24 2015The Lamperti--Kiu transformation for real-valued self-similar Markov processes (rssMp) states that, associated to each rssMp via a space-time transformation, there is a Markov additive process (MAP). In the case that the rssMp is taken to be an $\alpha$-stable ... More

Spectrally negative Levy processes perturbed by functionals of their running supremumApr 07 2012In the setting of the classical Cramer-Lundberg risk insurance model, Albrecher and Hipp (2007) introduced the idea of tax payments. More precisely, if $X = \{X_t : t\geq 0\}$ represents the Cramer-Lundberg process and, for all $t\geq 0$, $S_t = \sup_{s\leq ... More

A capped optimal stopping problem for the maximum processApr 13 2012This paper concerns an optimal stopping problem driven by the running maximum of a spectrally negative Levy process X. More precisely, we are interested in capped versions of the American lookback optimal stopping problem, which has its origins in mathematical ... More

Perpetual Integrals for Levy ProcessesJan 04 2015We ask for necessary and sufficient conditions for almost sure finiteness of the perpetual integrals of a Levy process. Zero-one laws are already known for Brownian motion with drift and spectrally one-sided Levy processes. Under the assumption that local ... More

Survival of homogeneous fragmentation processes with killingApr 27 2011Aug 20 2012We consider a homogenous fragmentation process with killing at an exponential barrier. With the help of two families of martingales we analyse the growth of the largest fragment for parameter values that allow for survival. In this respect the present ... More

The Seneta-Heyde scaling for homogeneous fragmentationsJul 06 2015Homogeneous mass fragmentation processes describe the evolution of a unit mass that breaks down randomly into pieces as time. Mathematically speaking, they can be thought of as continuous-time analogues of branching random walks with non-negative displacements. ... More

General tax structures and the Levy insurance risk modelFeb 25 2009In the spirit of previous of Albrecher, Hipp, Renaud and Zhou we consider a L\'evy insurance risk model with tax payments of a more general structure than in the aforementioned papers that was also considered in \cite{ABBR}. In terms of scale functions, ... More

Refracted Levy processesJan 30 2008May 12 2008Motivated by classical considerations from risk theory, we investigate boundary crossing problems for refracted L\'evy processes. The latter is a L\'evy process whose dynamics change by subtracting off a fixed linear drift (of suitable size) whenever ... More

Entrance and exit at infinity for stable jump diffusionsFeb 05 2018In his seminal work from the 1950s, William Feller classified all one-dimensional diffusions on $-\infty\leq a<b\leq \infty$ in terms of their ability to access the boundary (Feller's test for explosions) and to enter the interior from the boundary. Feller's ... More

The total mass of super-Brownian motion upon exiting balls and Sheu's compact support conditionAug 07 2013We study the total mass of a d-dimensional super-Brownian motion as it first exits an increasing sequence of balls. The process of the total mass is a time-inhomogeneous continuous-state branching process, where the increasing radii of the balls are taken ... More

The theory of scale functions for spectrally negative Le vy processesApr 07 2011The purpose of this review article is to give an up to date account of the theory and application of scale functions for spectrally negative Levy processes. Our review also includes the first extensive overview of how to work numerically with scale functions. ... More

An optimal stopping problem for fragmentation processesJan 26 2011In this article we consider a toy example of an optimal stopping problem driven by fragmentation processes. We show that one can work with the concept of stopping lines to formulate the notion of an optimal stopping problem and moreover, to reduce it ... More

Unbiased `walk-on-spheres' Monte Carlo methods for the fractional LaplacianSep 11 2016Sep 13 2016We consider Monte Carlo methods for simulating solutions to the analogue of the Dirichlet problem in which the Laplacian is replaced by the fractional Laplacian. Specifically we consider the analogue of the so-called `walk-on-spheres' algorithm. In the ... More

More on hypergeometric Levy processesSep 08 2015Kuznetsov et al. (2011) and Kuznetsov and Pardo (2013) introduced the family of Hypergeometric L\'evy processes. They appear naturally in the study of fluctuations of stable processes when one analyses stable processes through the theory of positive self-similar ... More

Real Self-Similar Processes Started from the OriginJan 04 2015Since the seminal work of Lamperti there is a lot of interest in the understanding of the general structure of self-similar Markov processes. Lamperti gave a representation of positive self-similar Markov processes with initial condition strictly larger ... More

Skeletal stochastic differential equations for superprocessesApr 11 2019Apr 16 2019It is well understood that a supercritical superprocess is equal in law to a discrete Markov branching process whose genealogy is dressed in a Poissonian way with immigration which initiates subcritial superprocesses. The Markov branching process corresponds ... More

Deep factorisation of the stable process II; potentials and applicationsNov 19 2015Here we propose a different perspective of the deep factorisation in Kyprianou (2015) based on determining potentials. Indeed, we factorise the inverse of the MAP-exponent associated to a stable process via the Lamperti-Kiu transform. Here our factorisation ... More

Unbiased `walk-on-spheres' Monte Carlo methods for the fractional LaplacianSep 11 2016Jun 24 2017We consider Monte Carlo methods for simulating solutions to the analogue of the Dirichlet boundary-value problem in which the Laplacian is replaced by the fractional Laplacian and boundary conditions are replaced by conditions on the exterior of the domain. ... More

The prolific backbone for supercritical superdiffusionsDec 23 2009Sep 21 2010We develop an idea of Evans and O'Connell, Englander and Pinsky and Duquesne and Winkel by giving a pathwise construction of the so called `backbone' decomposition for supercritical superprocesses. Our results also complement a related result for critical ... More

Branching Brownian motion in strip: survival near criticalityDec 06 2012We consider a branching Brownian motion with linear drift in which particles are killed on exiting the interval (0,K) and study the evolution of the process on the event of survival as the width of the interval shrinks to the critical value at which survival ... More

On the excursions of reflected local time processes and stochastic fluid queuesJun 10 2010This paper extends previous work by the authors. We consider the local time process of a strong Markov process, add negative drift, and reflect it \`a la Skorokhod. The resulting process is used to model a fluid queue. We derive an expression for the ... More

A transformation for Lévy processes with one-sided jumps and applicationsOct 19 2010The aim of this work is to extend and study a family of transformations between Laplace exponents of L\'evy processes which have been introduced recently in a variety of different contexts by Patie, Kyprianou and Patie, and, Gnedin, as well as in older ... More

Skeletal stochastic differential equations for continuous-state branching processFeb 12 2017Apr 15 2019It is well understood that a supercritical continuous-state branching process (CSBP) is equal in law to a discrete continuous-time Galton Watson process (the skeleton of prolific individuals) whose edges are dressed in a Poissonian way with immigration ... More

Special, conjugate and complete scale functions for spectrally negative Lévy processesDec 20 2007Following from recent developments by Hubalek and Kyprianou, the objective of this paper is to provide further methods for constructing new families of scale functions for spectrally negative L\'evy processes which are completely explicit. This is the ... More

Conditioning subordinators embedded in Markov processesJun 25 2015Jun 23 2016The running infimum of a Levy process relative to its point of issue is know to have the same range that of the negative of a certain subordinator. Conditioning a Levy process issued from a strictly positive value to stay positive may therefore be seen ... More

Skeletal stochastic differential equations for continuous-state branching processFeb 12 2017Dec 22 2017It is well understood that a supercritical continuous-state branching process (CSBP) is equal in law to a discrete continuous-time Galton Watson process (the skeleton of prolific individuals) whose edges are dressed in a Poissonian way with immigration ... More

Stable Lévy processes in a coneApr 23 2018Jun 08 2018Ba\~nuelos and Bogdan (2004) and Bogdan, Palmowski and Wang (2016) analyse the asymptotic tail distribution of the first time a stable (L\'evy) process in dimension $d\geq 2$ exists a cone. We use these results to develop the notion of a stable process ... More

Stable processes conditioned to avoid an intervalFeb 20 2018Feb 21 2018Conditioning Markov processes to avoid a domain is a classical problem that has been studied in many settings. Ingredients for standard arguments involve the leading order tail asymptotics of the distribution of the first hitting time of the domain of ... More

Spines, skeletons and the Strong Law of Large Numbers for superdiffusionsSep 24 2013Consider a supercritical superdiffusion (X_t) on a domain D subset R^d with branching mechanism -\beta(x) z+\alpha(x) z^2 + int_{(0,infty)} (e^{-yz}-1+yz) Pi(x,dy). The skeleton decomposition provides a pathwise description of the process in terms of ... More

Stochastic Methods for the Neutron Transport Equation I: Linear Semigroup asymptoticsOct 03 2018Jan 01 2019The Neutron Transport Equation (NTE) describes the flux of neutrons through an inhomogeneous fissile medium. In this paper, we reconnect the NTE to the physical model of the spatial Markov branching process which describes the process of nuclear fission, ... More

Stochastic Methods for the Neutron Transport Equation II: Almost sure growthJan 01 2019The neutron transport equation (NTE) describes the flux of neutrons across a planar cross-section in an inhomogeneous fissile medium when the process of nuclear fission is active. Classical work on the NTE emerges from the applied mathematics literature ... More

Ruin Probabilities and Overshoots for General Levy Insurance Risk ProcessesMar 24 2005We formulate the insurance risk process in a general Levy process setting, and give general theorems for the ruin probability and the asymptotic distribution of the overshoot of the process above a high level, when the process drifts to -\infty a.s. and ... More

Multilevel Monte Carlo simulation for Levy processes based on the Wiener-Hopf factorisationOct 22 2012Apr 12 2013In Kuznetsov et al. (2011) a new Monte Carlo simulation technique was introduced for a large family of Levy processes that is based on the Wiener-Hopf decomposition. We pursue this idea further by combining their technique with the recently introduced ... More

A phase transition in excursions from infinity of the "fast" fragmentation-coalescence processFeb 16 2016An important property of Kingman's coalescent is that, starting from a state with an infinite number of blocks, over any positive time horizon, it transitions into an almost surely finite number of blocks. This is known as `coming down from infinity'. ... More

Almost sure growth of supercritical multi-type continuous state branching processJul 16 2017Feb 21 2018In Li (2011), Example 2.2, the notion of a multi-type continuous-state branching process (MCSBP) was introduced with a finite number of types, with the countably infinite case being proposed in Kyprianou and Palau (2017). One may consider such processes ... More

A phase transition in excursions from infinity of the "fast" fragmentation-coalescence processFeb 16 2016Jan 17 2017An important property of Kingman's coalescent is that, starting from a state with an infinite number of blocks, over any positive time horizon, it transitions into an almost surely finite number of blocks. This is known as `coming down from infinity'. ... More

Double hypergeometric Lévy processes and self-similarityApr 12 2019Motivated by a recent paper of Budd, where a new family of positive self-similar Markov processes associated to stable processes appears, we introduce a new family of L\'evy processes, called the double hypergeometric class, whose Wiener-Hopf factorisation ... More

Meromorphic Levy processes and their fluctuation identitiesApr 26 2010Apr 09 2011The last couple of years has seen a remarkable number of new, explicit examples of the Wiener-Hopf factorization for Levy processes where previously there had been very few. We mention in particular the many cases of spectrally negative Levy processes, ... More

Occupation times of refracted Lévy processesMay 03 2012A refracted L\'evy process is a L\'evy process whose dynamics change by subtracting off a fixed linear drift (of suitable size) whenever the aggregate process is above a pre-specified level. More precisely, whenever it exists, a refracted L\'evy process ... More

Optimal control with absolutely continuous strategies for spectrally negative Levy processesAug 13 2010In the last few years there has been renewed interest in the classical control problem of de Finetti for the case that underlying source of randomness is a spectrally negative Levy process. In particular a significant step forward is made in an article ... More

Conditioned real self-similar Markov processesOct 06 2015In recent work, Chaumont et al. [9] showed that is possible to condition a stable process with index ${\alpha} \in (1,2)$ to avoid the origin. Specifically, they describe a new Markov process which is the Doob h-transform of a stable process and which ... More

Extinction properties of multi-type continuous-state branching processesApr 14 2016Jan 22 2018Recently in Barczy, Li and Pap (2015), the notion of a multi-type continuous-state branching process (with immigration) having d-types was introduced as a solution to an d-dimensional vector- valued SDE. Preceding that, work on affine processes, originally ... More

Extinction properties of multi-type continuous-state branching processesApr 14 2016Apr 19 2016Recently in Barczy, Li and Pap (2015), the notion of a multi-type continuous-state branching process (with immigration) having d-types was introduced as a solution to an d-dimensional vector- valued SDE. Preceding that, work on affine processes, originally ... More

An Euler-Poisson Scheme for Lévy driven SDEsSep 07 2013We describe an Euler scheme to approximate solutions of L\'evy driven Stochastic Differential Equations (SDE) where the grid points are random and given by the arrival times of a Poisson process. This result extends a previous work of the authors in Ferreiro-Castilla ... More

Hitting distributions of alpha-stable processes via path censoring and self-similarityDec 15 2011Jul 13 2012In this paper we return to the problem of Blumenthal-Getoor-Ray, published in 1961, which gave the law of the position of first entry of a symmetric alpha-stable process into the unit ball. Specifically, we are interested in establishing the same law, ... More

Universality in a class of fragmentation-coalescence processesApr 13 2015We introduce and analyse a class of fragmentation-coalescence processes defined on finite systems of particles organised into clusters. Coalescent events merge multiple clusters simultaneously to form a single larger cluster, while fragmentation breaks ... More

Universality in a class of fragmentation-coalescence processesApr 13 2015Jan 30 2017We introduce and analyse a class of fragmentation-coalescence processes defined on finite systems of particles organised into clusters. Coalescent events merge multiple clusters simultaneously to form a single larger cluster, while fragmentation breaks ... More

Strong Law of Large Numbers for branching diffusionsSep 03 2007Let $X$ be the branching particle diffusion corresponding to the operator $Lu+\beta (u^{2}-u)$ on $D\subseteq \mathbb{R}^{d}$ (where $\beta \geq 0$ and $\beta\not\equiv 0$). Let $\lambda_{c}$ denote the generalized principal eigenvalue for the operator ... More

Entrance laws at the origin of self-similar Markov processes in high dimensionsDec 05 2018In this paper we consider the problem of finding entrance laws at the origin for self-similar Markov processes in $\mathbb{R}^d$, killed upon hitting the origin. Under mild assumptions, we show the existence of an entrance law and the convergence to this ... More

The UK financial mathematics M.ScMay 26 2014May 29 2014Postgraduate taught degrees in financial mathematics have been booming in popularity in the UK for the last 20 years. The fees for these courses are considerably higher than other comparable masters-level courses. Why? Vendors stipulate that they offer ... More

Old and new examples of scale functions for spectrally negative Levy processesDec 29 2007Jul 04 2008We give a review of the state of the art with regard to the theory of scale functions for spectrally negative Levy processes. From this we introduce a general method for generating new families of scale functions. Using this method we introduce a new ... More

A Ciesielski-Taylor type identity for positive self-similar Markov processesAug 08 2009Dec 13 2010The aim of this note is to give a straightforward proof of a general version of the Ciesielski-Taylor identity for positive self-similar Markov processes of the spectrally negative type which umbrellas all previously known Ciesielski-Taylor identities ... More

Multi-species neutron transport equationSep 04 2018Jan 03 2019The Neutron Transport Equation (NTE) describes the flux of neutrons through inhomogeneous fissile medium. Whilst well treated in the nuclear physics literature (cf. [9, 27]), the NTE has had a somewhat scattered treatment in mathematical literature with ... More

The hitting time of zero for a stable processDec 20 2012Mar 10 2014For any two-sided jumping $\alpha$-stable process, where $1 < \alpha < 2$, we find an explicit identity for the law of the first hitting time of the origin. This complements existing work in the symmetric case and the spectrally one-sided case; cf. Yano-Yano-Yor ... More

Stable windings at the originMay 23 2016Sep 26 2016In 1996, Bertoin and Werner [5] demonstrated a functional limit theorem, characterising the windings of pla- nar isotropic stable processes around the origin for large times, thereby complementing known results for planar Brownian mo- tion. The question ... More

Smoothness of scale functions for spectrally negative Levy processesMar 08 2009Scale functions play a central role in the fluctuation theory of spectrally negative L\'evy processes and often appear in the context of martingale relations. These relations are often complicated to establish requiring excursion theory in favour of It\^o ... More

On optimal dividends in the dual modelNov 30 2012Jun 04 2013We revisit the dividend payment problem in the dual model of Avanzi et al. ([2], [1], and [3]). Using the fluctuation theory of spectrally positive L\'{e}vy processes, we give a short exposition in which we show the optimality of barrier strategies for ... More

Branching processes in random environment die slowlyApr 07 2008Let $Z_{n,}n=0,1,...,$ be a branching process evolving in the random environment generated by a sequence of iid generating functions $% f_{0}(s),f_{1}(s),...,$ and let $S_{0}=0,S_{k}=X_{1}+...+X_{k},k\geq 1,$ be the associated random walk with $X_{i}=\log ... More

Stable windings at the originMay 23 2016Jan 31 2018In 1996, Bertoin and Werner [5] demonstrated a functional limit theorem, characterising the windings of pla- nar isotropic stable processes around the origin for large times, thereby complementing known results for planar Brownian mo- tion. The question ... More

Some remarks on first passage of Levy processes, the American put and pasting principlesAug 25 2005The purpose of this article is to provide, with the help of a fluctuation identity, a generic link between a number of known identities for the first passage time and overshoot above/below a fixed level of a Levy process and the solution of Gerber and ... More

Optimal prediction for positive self-similar Markov processesSep 07 2014This paper addresses the question of predicting when a positive self-similar Markov process X attains its pathwise global supremum or infimum before hitting zero for the first time (if it does at all). This problem has been studied in Glover et al. (2013) ... More

The largest fragment of a homogeneous fragmentation processMar 23 2016We show that in homogeneous fragmentation processes the largest fragment at time $t$ has size $e^{-t \Phi'(\bar{p})}t^{-\frac32 (\log \Phi)'(\bar{p})+o(1)},$ where $\Phi$ is the L\'evy exponent of the fragmentation process, and $\bar{p}$ is the unique ... More

The largest fragment of a homogeneous fragmentation processMar 23 2016Nov 03 2016We show that in homogeneous fragmentation processes the largest fragment at time $t$ has size $e^{-t \Phi'(\bar{p})}t^{-\frac32 (\log \Phi)'(\bar{p})+o(1)},$ where $\Phi$ is the L\'evy exponent of the fragmentation process, and $\bar{p}$ is the unique ... More

Optimal dividends in the dual model under transaction costsJan 31 2013Nov 11 2013We analyze the optimal dividend payment problem in the dual model under constant transaction costs. We show, for a general spectrally positive L\'{e}vy process, an optimal strategy is given by a $(c_1,c_2)$-policy that brings the surplus process down ... More

On continuous state branching processes: conditioning and self-similarityDec 06 2007In this paper, for $\alpha\in (1, 2}$ we show that the $\alpha$-stable continuous-state branching process and the associated process conditioned never to become extinct are positive self-similar Markov processes. Understanding the interaction of the Lamperti ... More

Backbone decomposition for continuous-state branching processes with immigrationJun 10 2011In the spirit of Duqesne and Winkel (2007) and Berestycki et al. (2011) we show that supercritical continuous-state branching process with a general branching mechanism and general immigration mechanism is equal in law to a continuous-time Galton Watson ... More

Convexity and smoothness of scale functions and de Finetti's control problemJan 13 2008Aug 25 2008Under appropriate conditions, we obtain smoothness and convexity properties of $q$-scale functions for spectrally negative L\'evy processes. Our method appeals directly to very recent developments in the theory of potential analysis of subordinators. ... More

Some explicit identities associated with positive self-similar Markov processesAug 17 2007We consider some special classes of L\'evy processes with no gaussian component whose L\'evy measure is of the type $\pi(dx)=e^{\gamma x}\nu(e^x-1) dx$, where $\nu$ is the density of the stable L\'evy measure and $\gamma$ is a positive parameter which ... More

Fluctuation theory and exit systems for positive self-similar Markov processesDec 13 2008Dec 07 2012For a positive self-similar Markov process, X, we construct a local time for the random set, $\Theta$, of times where the process reaches its past supremum. Using this local time we describe an exit system for the excursions of X out of its past supremum. ... More

Overshoots and undershoots of Lévy processesMar 09 2006We obtain a new fluctuation identity for a general L\'{e}vy process giving a quintuple law describing the time of first passage, the time of the last maximum before first passage, the overshoot, the undershoot and the undershoot of the last maximum. With ... More

Potentials of stable processesDec 04 2013For a stable process, we give an explicit formula for the potential measure of the process killed outside a bounded interval and the joint law of the overshoot, undershoot and undershoot from the maximum at exit from a bounded interval. We obtain the ... More

New families of subordinators with explicit transition probability semigroupFeb 05 2014Jul 04 2014There exist only a few known examples of subordinators for which the transition probability density can be computed explicitly along side an expression for its L\'evy measure and Laplace exponent. Such examples are useful in several areas of applied probability, ... More

Analysis of stochastic fluid queues driven by local time processesSep 10 2007We consider a stochastic fluid queue served by a constant rate server and driven by a process which is the local time of a certain Markov process. Such a stochastic system can be used as a model in a priority service system, especially when the time scales ... More

The Gapeev-Kühn stochastic game driven by a spectrally positive Lévy processApr 24 2009In Gapeev and K\"uhn (2005), the stochastic game corresponding to perpetual convertible bonds was considered when driven by a Brownian motion and a compound Poisson process with exponential jumps. We consider the same stochastic game but driven by a spectrally ... More

Traveling waves and homogeneous fragmentationNov 27 2009Dec 28 2011We formulate the notion of the classical Fisher-Kolmogorov-Petrovskii-Piscounov (FKPP) reaction diffusion equation associated with a homogeneous conservative fragmentation process and study its traveling waves. Specifically, we establish existence, uniqueness ... More

The backbone decomposition for spatially dependent supercritical superprocessesApr 07 2013Consider any supercritical Galton-Watson process which may become extinct with positive probability. It is a well-understood and intuitively obvious phenomenon that, on the survival set, the process may be pathwise decomposed into a stochastically `thinner' ... More

The extended hypergeometric class of Lévy processesOct 03 2013May 09 2014With a view to computing fluctuation identities related to stable processes, we review and extend the class of hypergeometric L\'evy processes explored in Kuznetsov and Pardo (arXiv:1012.0817). We give the Wiener-Hopf factorisation of a process in the ... More

Strong Law of Large Numbers for Fragmentation ProcessesSep 17 2008In the spirit of a classical results for Crump-Mode-Jagers processes, we prove a strong law of large numbers for homogenous fragmentation processes. Specifically, for self-similar fragmentation processes, including homogenous processes, we prove the almost ... More

A Wiener--Hopf Monte Carlo simulation technique for Lévy processesDec 23 2009Feb 17 2012We develop a completely new and straightforward method for simulating the joint law of the position and running maximum at a fixed time of a general L\'{e}vy process with a view to application in insurance and financial mathematics. Although different, ... More

Supercritical super-Brownian motion with a general branching mechanism and travelling wavesMay 20 2010Apr 05 2011We consider the classical problem of existence, uniqueness and asymptotics of monotone solutions to the travelling wave equation associated to the parabolic semi-group equation of a super-Brownian motion with a general branching mechanism. Whilst we are ... More

Chaotic scattering from pinball machine like systemsNov 14 1998Dec 29 1999We study a model inspired by the pinball machine involving chaotic scattering of particles on hard disks with inelasticity. This system exhibits sensitivity not only on the initial conditions of the scattering point particle but also on the external force ... More

Exact and asymptotic $n$-tuple laws at first and last passageNov 19 2008Jul 02 2009Understanding the space-time features of how a L\'evy process crosses a constant barrier for the first time, and indeed the last time, is a problem which is central to many models in applied probability such as queueing theory, financial and actuarial ... More

Near-optimal Nonmyopic Value of Information in Graphical ModelsJul 04 2012A fundamental issue in real-world systems, such as sensor networks, is the selection of observations which most effectively reduce uncertainty. More specifically, we address the long standing problem of nonmyopically selecting the most informative subset ... More

R-process and alpha-elements in the Galactic disk: Kinematic correlationsJul 11 2004Recent studies of elemental abundances in the Galactic halo and in the Galactic disk have underscored the possibility to kinematically separate different Galactic subcomponents. Correlations between the galactocentric rotation velocity and various element ... More

Search for an intrinsic metallicity spread in old globular clusters of the Large Magellanic CloudSep 05 2018We report for the first time on the magnitude of the intrinsic [Fe/H] spread among ten old globular clusters (GCs) of the Large Magellanic Cloud (LMC). Such spreads are merely observed in approximately five per cent of the Milky Way GCs and recently gained ... More

Weighted ${L^p}$-Liouville Theorems for Hypoelliptic Partial Differential Operators on Lie GroupsMar 05 2015We prove weighted $L^p$-Liouville theorems for a class of second order hypoelliptic partial differential operators $\mathcal{L}$ on Lie groups $\mathbb{G}$ whose underlying manifold is $n$-dimensional space. We show that a natural weight is the right-invariant ... More

Multivariate normal approximation of the maximum likelihood estimator via the delta methodSep 13 2016Aug 09 2018We use the delta method and Stein's method to derive, under regularity conditions, explicit upper bounds for the distributional distance between the distribution of the maximum likelihood estimator (MLE) of a $d$-dimensional parameter and its asymptotic ... More

Three disks in a row: A two-dimensional scattering analog of the double-well problemApr 02 1996Nov 01 1996We investigate the scattering off three nonoverlapping disks equidistantly spaced along a line in the two-dimensional plane with the radii of the outer disks equal and the radius of the inner disk varied. This system is a two-dimensional scattering analog ... More

Jacobi Elliptic Functions and the Complete Solution to the Bead on the Hoop ProblemJan 20 2012Jacobi elliptic functions are flexible functions that appear in a variety of problems in physics and engineering. We introduce and describe important features of these functions and present a physical example from classical mechanics where they appear: ... More

Characteristic and Ehrhart polynomialsJan 02 1998Let A be a subspace arrangement and let chi(A,t) be the characteristic polynomial of its intersection lattice L(A). We show that if the subspaces in A are taken from L(B_n), where B_n is the type B Weyl arrangement, then chi(A,t) counts a certain set ... More

Multivariate normal approximation of the maximum likelihood estimator via the delta methodSep 13 2016We use the delta method and Stein's method to derive, under regularity conditions, explicit upper bounds for the distributional distance between the distribution of the maximum likelihood estimator (MLE) of a $d$-dimensional parameter and its asymptotic ... More

Nematicity, magnetism and superconductivity in FeSeNov 17 2017Iron-based superconductors are well known for their complex interplay between structure, magnetism and superconductivity. FeSe offers a particularly fascinating example. This material has been intensely discussed because of its extended nematic phase, ... More

Network coding with modular latticesSep 03 2010In [1], K\"otter and Kschischang presented a new model for error correcting codes in network coding. The alphabet in this model is the subspace lattice of a given vector space, a code is a subset of this lattice and the used metric on this alphabet is ... More

Diffraction and near-zero transmission of flexural phonons at graphene grain boundariesFeb 18 2015Graphene grain boundaries are known to affect phonon transport and thermal conductivity, suggesting that they may be used to engineer the phononic properties of graphene. Here, the effect of two buckled grain boundaries on long-wavelength flexural acoustic ... More

An application of the backbone decomposition to supercritical super-Brownian motion with a barrierAug 22 2011Feb 07 2012We analyse the behaviour of supercritical super-Brownian motion with a barrier through the pathwise backbone embedding of Berestycki et al. (2011). In particular, by considering existing results for branching Brownian motion due to Harris et al. (2006) ... More

Scattering of flexural acoustic phonons at grain boundaries in grapheneApr 30 2014We investigate the scattering of long-wavelength flexural phonons against grain boundaries in graphene using molecular dynamics simulations. Three symmetric tilt grain boundaires are considered: one with a misorientation angle of $17.9^\circ$ displaying ... More

Mobius functions of latticesJan 02 1998We introduce the concept of a bounded below set in a lattice. This can be used to give a generalization of Rota's broken circuit theorem to any finite lattice. We then show how this result can be used to compute and combinatorially explain the M\"obius ... More

Numerical Approximation of Fractional Powers of Regularly Accretive OperatorsAug 24 2015Jul 14 2016We study the numerical approximation of fractional powers of accretive operators in this paper. Namely, if $A$ is the accretive operator associated with an accretive sesquilinear form $A(\cdot,\cdot)$ defined on a Hilbert space $\mathbb V$ contained in ... More

Numerical Approximation of Fractional Powers of Elliptic OperatorsJul 03 2013Sep 03 2013We present and study a novel numerical algorithm to approximate the action of $T^\beta:=L^{-\beta}$ where $L$ is a symmetric and positive definite unbounded operator on a Hilbert space $H_0$. The numerical method is based on a representation formula for ... More

Sliding Over a Phase TransitionMay 24 2011The effects of a displacive structural phase transition on sliding friction are in principle accessible to nanoscale tools such as the Atomic Force Microscopy, yet they are still surprisingly unexplored. We present model simulations demonstrating and ... More