English

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

Probability 2022-08-17 v1

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.

Keywords

Cite

@article{arxiv.2208.07668,
  title  = {Invariant measures of L\'evy-type operators and their associated Markov processes},
  author = {Anita Behme and David Oechsler},
  journal= {arXiv preprint arXiv:2208.07668},
  year   = {2022}
}