On Markovian semigroups of Lévy driven SDEs, symbols and pseudo--differential operators

Abstract

We analyse analytic properties of nonlocal transition semigroups associated with a class of stochastic differential equations (SDEs) in ${\mathbb{R}}^d$ driven by pure jump--type Lévy processes. First, we will show under which conditions the semigroup will be analytic on the Besov space $B_{p,q}^m({\mathbb{R}}^d)$ with $1\le p,q<\infty$ and $m\in \mathbb{R}$. Secondly, we present some applications by proving the strong Feller property and give weak error estimates for approximating schemes of the SDEs over the Besov space $B_{\infty ,\infty }^m({\mathbb{R}}^d)$.

References in corpus (3)

• Tempered stable distributions and processes
• On subordination of holomorphic semigroups
• Sobolev index: A classification of Lévy processes

Cited by in corpus (1)

• A Carleman estimate for the fractional heat equation and its application in final state observability