Stochastic systems provide powerful abstract models for a variety of important real-life
applications: for example, power supply, traffic flow, data transmission. They (and the real …

Sufficient conditions for a symmetric jump-diffusion process to be conservative and recurrent
are given in terms of the volume of the state space and the jump kernel of the process. A …

We study the existence of (Markovian) solutions to the (A,C_c^∞(R^d))-martingale problem
associated with the Lévy-type operator A with symbol q(x,ξ). Firstly, we establish conditions …

Suppose that d\ge1 and 0<β<α<2. We establish the existence and uniqueness of the
fundamental solution q^b(t,x,y) to a class of (typically non-symmetric) non-local operators …

In this paper, we consider a long-time behavior of stable-like processes. A stable-like
process is a Feller process given by the symbol p (x, ξ)=− iβ (x) ξ+ γ (x)| ξ| α (x), where α …

We prove a result on the fractional Sobolev regularity of composition of paths of low
fractional Sobolev regularity with functions of bounded variation. The result relies on the …

In this paper, we study the homogenization of a diffusion process with jumps, that is, Feller
process generated by an integro-differential operator. This problem is closely related to the …

In this note we prove some sufficient conditions for transience and recurrence of a Lévy-type
process in $\mathbb {R} $, whose generator defined on the test functions is of the form\begin …

The probabilistic symbol is defined as the right-hand side derivative at time zero of the
characteristic functions corresponding to the one-dimensional marginals of a time …

In the development of stochastic integration and the theory of semimartingales, Markov
processes have been a constant source of inspiration. Despite this historical interweaving, it …