Symmetric Lévy processes with reflection
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
Details
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