Related papers: Exact Edgeworth expansion for a L\'{e}vy process
The reflected process of a random walk or L\'evy process arises in many areas of applied probability, and a question of particular interest is how the tail of the distribution of the heights of the excursions away from zero behaves…
We show on- and off-diagonal upper estimates for the transition densities of symmetric Levy and Levy-type processes. To get the an-diagonal estimates we prove a Nash type inequality for the related Dirichlet form. For the off-diagonal…
The aim of this short note is to present the notion of IDT processes, which is a wide generalization of L\'{e}vy processes obtained from a modified infinitely divisible property. Special attention is put on a number of examples, in order to…
We provide a novel expression of the scale function for a L\'evy processes with negative phase-type jumps. It is in terms of a certain transition rate matrix which is explicit up to a single positive number. A monotone iterative scheme for…
Upper estimates of densities of convolution semigroups of probability measures are given under explicit assumptions on the corresponding L\'evy measure and the L\'evy--Khinchin exponent.
The nonextensitivity parameter $q$ occuring in some of the applications of Tsallis statistics (known also as index of the corresponding L\'evy distribution) is shown to be given, in $q>1$ case, entirely by the fluctuations of the parameters…
We derive explicit formulas for the Mellin transform and the distribution of the exponential functional for Levy processes with rational Laplace exponent. This extends recent results by Cai and Kou on the processes with hyper-exponential…
We identify a necessary and sufficient condition for a L\'evy white noise to be a tempered distribution. More precisely, we show that if the L\'evy measure associated with this noise has a positive absolute moment, then the L\'evy white…
Conditions are given, sufficient for the distribution of an Ornstein-Uhlenbeck process with L\'evy noise to be absolutely continuous or to possess a smooth density. For the processes with non-degenerate drift coefficient, these conditions…
A quasi-infinitely divisible distribution on $\mathbb{R}$ is a probability distribution whose characteristic function allows a L\'evy-Khintchine type representation with a "signed L\'evy measure", rather than a L\'evy measure.…
The aim of this article is to provide a scheme for simulating diffusion processes evolving in one-dimensional discontinuous media. This scheme does not rely on smoothing the coefficients that appear in the infinitesimal generator of the…
We study stochastic differential equations (SDEs) of McKean-Vlasov type with distribution dependent drifts and driven by pure jump L\'{e}vy processes. We prove a uniform in time propagation of chaos result, providing quantitative bounds on…
Exotic stochastic processes are shown to emerge in the quantum evolution of complex systems. Using influence function techniques, we consider the dynamics of a system coupled to a chaotic subsystem described through random matrix theory. We…
We give new proofs of certain equivalent conditions for the existence of generalized moments of a L\'evy process $(X_t)_{t\geq 0}$; in particular, the existence of a generalized $g$-moment is equivalent to the uniform integrability of…
Random walk is a fundamental concept with applications ranging from quantum physics to econometrics. Remarkably, one specific model of random walks appears to be ubiquitous across many fields as a tool to analyze transport phenomena in…
Probability distributions defined on the half space are known to be quite different from those in the full space. Here, a nonextensive entropic treatment is presented for the half space in an analytic and self-consistent way. In this…
We propose isomorphism type identities for nonlinear functionals of general infinitely divisible processes. Such identities can be viewed as an analogy of the Cameron-Martin formula for Poissonian infinitely divisible processes but with…
Levy distributions are involved in many physical phenomenon. The purpose of our study is to understand metal insulator transitions in composite systems using the above distributions. The exact method (EM) based on the calculation of…
The law of a positive infinitely divisible process with no drift is characterized by its L\'evy measure on the paths space. Based on recent results of the two authors, it is shown that even for simple examples of such processes, the…
Let $(\xi,\eta)$ be a bivariate L\'evy process such that the integral $\int\_0^\infty e^{-\xi\_{t-}} d\eta\_t$ converges almost surely. We characterise, in terms of their \LL measures, those L\'evy processes for which (the distribution of)…