Coupling and exponential ergodicity for stochastic differential equations driven by Lévy processes

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Abstract

We present a novel idea for a coupling of solutions of stochastic differential equations driven by Lévy noise, inspired by some results from the optimal transportation theory. Then we use this coupling to obtain exponential contractivity of the semigroups associated with these solutions with respect to an appropriately chosen Kantorovich distance. As a corollary, we obtain exponential convergence rates in the total variation and standard L1-Wasserstein distances.

Original languageEnglish
Pages (from-to)4083-4125
Number of pages43
JournalStochastic Processes and their Applications
Volume127
Issue number12
Early online date3 Apr 2017
DOIs
Publication statusPublished - Dec 2017

Keywords

  • Couplings
  • Exponential ergodicity
  • Lévy processes
  • Stochastic differential equations
  • Wasserstein distances

ASJC Scopus subject areas

  • Statistics and Probability
  • Modelling and Simulation
  • Applied Mathematics

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