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arXiv · 2208.07668

Invariant measures of L\'evy-type operators and their associated Markov processes

Anita Behme·David Oechsler
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Abstract

A distributional equation as a criterion for invariant measures of Markov processes associated to L\'evy-type operators is established. This is obtained via a characterization of infinitesimally invariant measures of the associated generators. Particular focus is put on the one-dimensional case where the distributional equation becomes a Volterra-Fredholm integral equation, and on solutions to L\'evy-driven stochastic differential equations. The results are accompanied by various illustrative examples.

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Anita Behme, David Oechsler. 2022-08-16. Invariant measures of L\'evy-type operators and their associated Markov processes. https://arxiv.org/abs/2208.07668

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