Related papers: Intrinsic Ultracontractivity for General L\'evy pr…
We prove the intrinsic ultracontractivity for the semigroup generated by a large class of symmetric Levy processes such that the Levy measure satisfies some conditions in the neighborhood of 0, killed on exiting a bounded and connected…
Recently we extended the concept of intrinsic ultracontractivity to non-symmetric semigroups and proved that for a large class of non-symmetric diffusions Z with measure-valued drift and potential, the semigroup of Z^D (the process obtained…
For a symmetric $\alpha$-stable process $X$ on $\RR^n$ with $0<\alpha <2$, $n\geq 2$ and a domain $D \subset \RR^n$, let $L^D$ be the infinitesimal generator of the subprocess of $X$ killed upon leaving $D$. For a Kato class function $q$,…
Recently, in [Preprint (2006)], we extended the concept of intrinsic ultracontractivity to nonsymmetric semigroups. In this paper, we study the intrinsic ultracontractivity of nonsymmetric diffusions with measure-valued drifts and…
Let $X(t)$, $t\geq0$, be a L\'evy process in $\mathbb{R}^d$ starting at the origin. We study the closed convex hull $Z_s$ of $\{X(t): 0\leq t\leq s\}$. In particular, we provide conditions for the integrability of the intrinsic volumes of…
We construct intrinsic on-and off-diagonal upper and lower estimates for the transition probability density of a L\'evy process in small time. By intrinsic we mean that such estimates reflect the structure of the characteristic exponent of…
In this paper we consider a large class of symmetric Markov processes $X=(X_t)_{t\ge0}$ on $\R^d$ generated by non-local Dirichlet forms, which include jump processes with small jumps of $\alpha$-stable-like type and with large jumps of…
We study spectral-theoretic properties of non-self-adjoint operators arising in the study of one-dimensional L\'evy processes with completely monotone jumps with a one-sided barrier. With no further assumptions, we provide an integral…
We characterize the small-time asymptotic behavior of the exit probability of a L\'evy process out of a two-sided interval and of the law of its overshoot, conditionally on the terminal value of the process. The asymptotic expansions are…
This paper studies the invertibility property of continuous time moving average processes driven by a L\'evy process. We provide of sufficient conditions for the recovery of the driving noise. Our assumptions are specified via the kernel…
It is proved that the two-sided exits of a Levy process are proper, i.e. not a.s. equal to their one-sided counterparts, if and only if said process is not a subordinator or the negative of a subordinator. Furthermore, Levy processes are…
We examine three equivalent constructions of a censored symmetric purely discontinuous L\'evy process on an open set $D$; via the corresponding Dirichlet form, through the Feynman-Kac transform of the L\'evy process killed outside of $D$…
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.…
We will prove that: (1) A symmetric free L\'evy process is unimodal if and only if its free L\'evy measure is unimodal; (2) Every free L\'evy process with boundedly supported L\'evy measure is unimodal in sufficiently large time. (2) is…
In this paper we prove the uniform boundary Harnack principle in general open sets for harmonic functions with respect to a large class of rotationally symmetric purely discontinuous L\'evy processes.
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…
The escape from a given domain is one of the fundamental problems in statistical physics and the theory of stochastic processes. Here, we explore properties of the escape of an inertial particle driven by L\'evy noise from a bounded domain,…
Motivated 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…
We study long time behavior of integrated trawl processes introduced by Barndorff-Nielsen. The trawl processes form a class of stationary infinitely divisible processes, described by an infinitely divisible random measure (L\'evy base) and…
In this paper we show that a non-local operator of certain type extends to the generator of a strong Markov process, admitting the transition probability density. For this transition probability density we construct the intrinsic upper and…