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

Mateusz B. Majka

doi:10.1016/j.spa.2017.03.020

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

Mateusz B. Majka

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27 Citations (Scopus)

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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 language	English
Pages (from-to)	4083-4125
Number of pages	43
Journal	Stochastic Processes and their Applications
Volume	127
Issue number	12
Early online date	3 Apr 2017
DOIs	https://doi.org/10.1016/j.spa.2017.03.020
Publication status	Published - 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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© 2017 Elsevier B.V.
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abstract = "We present a novel idea for a coupling of solutions of stochastic differential equations driven by L{\'e}vy 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.",

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AB - 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.

KW - Couplings

KW - Exponential ergodicity

KW - Lévy processes

KW - Stochastic differential equations

KW - Wasserstein distances

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M3 - Article

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JF - Stochastic Processes and their Applications

IS - 12

ER -

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

Abstract

Keywords

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