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

Mateusz B. Majka

Stochastic Processes and their Applications, 2017, vol. 127, issue 12, 4083-4125

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.

Keywords: Stochastic differential equations; Lévy processes; Exponential ergodicity; Couplings; Wasserstein distances (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (7)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:127:y:2017:i:12:p:4083-4125

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DOI: 10.1016/j.spa.2017.03.020

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