Related papers: Yaglom limit for unimodal L\'{e}vy processes

We prove in this article the existence of the Yaglom limit for Markov chains on discrete state spaces in the setting where the absorbing state is accessible from a single non-absorbing state. We use a representation of the trajectories of…

In this short paper we show a sufficient condition for the solvability of the Dirichlet problem at infinity in Riemannian cones (as defined below).This condition is related to a celebrated result of Milnor that classifies parabolic…

The one dimensional distribution of a L\'{e}vy process is not known in general even though its characteristic function is given by the famous L\'{e}vy-Khinchine theorem. This article gives an exact series representation for the one…

We prove a Chevet type inequality which gives an upper bound for the norm of an isotropic log-concave unconditional random matrix in terms of expectation of the supremum of "symmetric exponential" processes compared to the Gaussian ones in…

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…

Chaotic systems near black holes satisfy a universal bound, $\lambda \leq \kappa_H$ linking the Lyapunov coefficient $\lambda$ associated with unstable orbits to surface gravity $\kappa_H$ of the event horizon. A natural question is whether…

We consider the problem of finding a stopping time that minimises the $L^1$-distance to $\theta$, the time at which a L\'evy process attains its ultimate supremum. This problem was studied in [12] for a Brownian motion with drift and a…

Estimation methods for the L\'{e}vy density of a L\'{e}vy process are developed under mild qualitative assumptions. A classical model selection approach made up of two steps is studied. The first step consists in the selection of a good…

We study recurrence and transience for L\'{e}vy processes induced by topological transformation groups. In particular the transience-recurrence dichotomy in terms of potential measures is established and transience is shown to be equivalent…

We prove that if Y is a hypersurface of degree d in P^n with isolated singularities, then the log canonical threshold of (P^n,Y) is at least min{n/d,1}. Moreover, if d is at least n+1, then we have equality if and only if Y is the…

We obtain general lower estimates of transition densities of jump L\'evy processes. We use them for processes with L\'evy measures having bounded support, processes with exponentially decaying L\'evy measures for large times and for…

This paper considers discretization of the L\'evy process appearing in the Lamperti representation of a strictly positive self-similar Markov process. Limit theorems for the resulting approximation are established under some regularity…

We study the density of the supremum of a strictly stable L\'evy process. As was proved recently in F. Hubalek and A. Kuznetsov "A convergent series representation for the density of the supremum of a stable process" (Elect. Comm. in…

In this paper we obtain uniformly locally $L^{\infty}$-estimate of solutions to non-autonomous quasilinear system involving operators in divergence form and a family of nonlinearities that are allowed to grow also critically.

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…

We construct a Hunt process that can be described as an isotropic $\alpha$-stable L\'evy process reflected from the complement of a bounded open Lipschitz set. In fact, we introduce a new analytic method for concatenating Markov processes.…

We consider a continuous-time random walk which is defined as an interpolation of a random walk on a point process on the real line. The distances between neighboring points of the point process are i.i.d. random variables in the normal…

In this paper, we investigate the asymptotic behavior of continuous-state branching processes in a Brownian random environment (CBBRE) conditioned on non-extinction. For the subcritical case, we prove the existence of the Yaglom limit and…

Given a bounded Lipschitz domain $\omega\subset\mathbb{R}^{d-1}$ and a lower semicontinuous function $W:\mathbb{R}^N\to\mathbb{R}_+\cup\{+\infty\}$ that vanishes on a finite set and that is bounded from below by a positive constant at…

We obtain the lower bounds for ergodic convergence rates, including spectral gaps and convergence rates in strong ergodicity for time-changed symmetric L\'{e}vy processes by using harmonic function and reversible measure. As direct…