Related papers: Censored symmetric L\'evy processes

Strongly continuous semigroups of unital completely positive maps (i.e. quantum Markov semigroups or quantum dynamical semigroups) on compact quantum groups are studied. We show that quantum Markov semigroups on the universal or reduced…

In a setting, where only "exit measures" are given, as they are associated with an arbitrary right continuous strong Markov process on a separable metric space, we provide simple criteria for the validity of Harnack inequalities for…

We prove that a general (not necessarily symmetric) L\'evy process killed on exiting a bounded open set (without regular condition on the boundary) is intrinsically ultracontractive, provided that $B(0,R_0)\subseteq \rm{supp}(\nu)$ for some…

We discuss an impact of various (path-wise) reflection-from-the barrier scenarios upon confining properties of a paradigmatic family of symmetric $\alpha $-stable L\'{e}vy processes, whose permanent residence in a finite interval on a line…

In this short note we study homogenization of symmetric $d$-dimensional L\'evy processes. Homogenization of one-dimensional pure jump Markov processes has been investigated by Tanaka \emph{et al.} in 1992; their motivation was the work by…

In this paper we study the Martin boundary of open sets with respect to a large class of purely discontinuous symmetric L\'evy processes in ${\mathbb R}^d$. We show that, if $D\subset {\mathbb R}^d$ is an open set which is $\kappa$-fat at a…

In contrast to their seemingly simple and shared structure of independence and stationarity, L\'evy processes exhibit a wide variety of behaviors, from the self-similar Wiener process to piecewise-constant compound Poisson processes.…

In this paper we consider the Dirichlet form on the half-space $\mathbb{R}^d_+$ defined by the jump kernel $J(x,y)=|x-y|^{-d-\alpha}\mathcal{B}(x,y)$, where $\mathcal{B}(x,y)$ can be degenerate at the boundary. Unlike our previous works…

In this paper we consider weak Harnack inequality and H\"older regularity estimates for symmetric $\alpha$-stable L\'evy process in $\mathbb{R}^d$, $\alpha \in (0,2)$, $d\geq 2$. We consider a symmetric $\alpha$-stable L\'evy process $X$…

In this paper, we study the cut-off phenomenon under the total variation distance of $d$-dimensional Ornstein-Uhlenbeck processes which are driven by L\'evy processes. That is to say, under the total variation distance, there is an abrupt…

We prove the scale invariant Harnack inequality and regularity properties for harmonic functions with respect to an isotropic unimodal L\'{e}vy process with the characteristic exponent $\psi$ satisfying some scaling condition. We show sharp…

We prove a boundary Harnack inequality for jump-type Markov processes on metric measure state spaces, under comparability estimates of the jump kernel and Urysohn-type property of the domain of the generator of the process. The result holds…

Iksanov and Pilipenko (2023) defined a skew stable L\'{e}vy process as a scaling limit of a sequence of perturbed at $0$ symmetric stable L\'{e}vy processes (continuous-time processes). Here, we provide a simpler construction of the skew…

Starting with a transient irreducible diffusion process $X^0$ on a locally compact separable metric space $(D, d)$, one can construct a canonical symmetric reflected diffusion process $\bar X$ on a completion $D^*$ of $(D, d)$ through the…

We study a $d$-dimensional non-symmetric strictly $\alpha$-stable L\'{e}vy process $\mathbf{X}$, whose spherical density is bounded and bounded away from the origin. First, we give sharp two-sided estimates on the transition density of…

In this paper we study interior potential-theoretic properties of purely discontinuous Markov processes in proper open subsets $D\subset \mathbb{R}^d$. The jump kernels of the processes may be degenerate at the boundary in the sense that…

We give two-term small-time approximation for the trace of the Dirichlet heat kernel of bounded smooth domain for unimodal L\'evy processes satisfying the weak scaling conditions.

A subordinate Brownian motion is a L\'evy process which can be obtained by replacing the time of the Brownian motion by an independent subordinator. The infinitesimal generator of a subordinate Brownian motion is $-\phi(-\Delta)$, where…

Consider the symmetric non-local Dirichlet form $(D,\D(D))$ given by $$ D(f,f)=\int_{\R^d}\int_{\R^d}\big(f(x)-f(y)\big)^2 J(x,y)\,dx\,dy $$with $\D(D)$ the closure of the set of $C^1$ functions on $\R^d$ with compact support under the norm…

We show the existence of L\'evy-type stochastic processes in one space dimension with characteristic triplets that are either discontinuous at thresholds, or are stable-like with stability index functions for which the closures of the…