Symmetric Lévy processes with reflection

Authors: Pavel Ievlev

Published in: Global and Stochastic Analysis (2021)

Date: January 2021

Abstract

In this paper we give meaning to the notion of reflecting Levy process in a smooth domain $D$ in terms of the domain of its generator. In contrast with other approaches, we work with the classical Neumann conditions. The main idea is to construct a suitable continuation of an initial function $f$ defined on $D$ to $\mathbb{R}^d$, and then associate with it some Markov semi-group.

Keywords

Reflected processes, Symmetric Lévy processes, Markov semigroup, Lévy operator