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

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 $L^1$-Wasserstein distances.

40 pages, revised version, accepted for publication in Stochastic Processes and their Applications. The final manuscript is available at Elsevier via https://doi.org/10.1016/j.spa.2017.03.020

References in corpus (4)

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• $L^p$-Wasserstein distance for stochastic differential equations driven by Lévy processes
• Transportation inequalities for non-globally dissipative SDEs with jumps via Malliavin calculus and coupling
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Cited by in corpus (8)

• Transportation inequalities for non-globally dissipative SDEs with jumps via Malliavin calculus and coupling
• Refined basic couplings and Wasserstein-type distances for SDEs with Lévy noises
• Exponential ergodicity for SDEs and McKean-Vlasov processes with Lévy noise
• Markovian Maximal Coupling of Markov Processes
• Implementable coupling of Lévy process and Brownian motion
• Weak averaging principle for multiscale stochastic dynamical systems driven by stable processes
• Coupling approach for exponential ergodicity of stochastic Hamiltonian systems with Lévy noises
• On Sub-Geometric Ergodicity of Diffusion Processes