Markov processes represent a universal model for a large variety of real life random
evolutions. The wide flow of new ideas, tools, methods and applications constantly pours …

We consider stochastic differential equations which are driven by multidimensional Levy
processes. We show that the infinitesimal generator of the solution is a pseudo-differential …

This survey describes the method of approximation of operator semigroups, based on the
Chernoff theorem. We outline recent results in this domain as well as clarify relations …

A time and space inhomogeneous Markov process is a Feller evolution process, if the
corresponding evolution system on the continuous functions vanishing at infinity is strongly …

We study two equivalent characterizations of the strong Feller property for a Markov process
and of the associated sub-Markovian semigroup. One is described in terms of locally uniform …

A Feynman formula is a representation of a solution of an initial (or initial-boundary) value
problem for an evolution equation (or, equivalently, a representation of the semigroup …

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 …

Ito's construction of Markovian solutions to stochastic equations driven by a Lévy noise is
extended to nonlinear distribution dependent integrands aiming at the effective construction …

arXiv:1209.4096v1 [math.PR] 18 Sep 2012 Upper estimates of transition densities for stable-dominated
semigroups Page 1 arXiv:1209.4096v1 [math.PR] 18 Sep 2012 Upper estimates of transition …

We present a simple construction method for Feller processes and a framework for the
generation of sample paths of Feller processes. The construction is based on state space …