Gradient estimates and ergodicity for SDEs driven by multiplicative Lévy noises via coupling

Mingjie Liang and Jian Wang

Stochastic Processes and their Applications, 2020, vol. 130, issue 5, 3053-3094

Abstract: We consider SDEs driven by multiplicative pure jump Lévy noises, where Lévy processes are not necessarily comparable to α-stable-like processes. By assuming that the SDE has a unique strong solution, we obtain gradient estimates of the associated semigroup when the drift term is locally Hölder continuous, and we establish the ergodicity of the process both in the L1-Wasserstein distance and the total variation, when the coefficients are dissipative for large distances. The proof is based on a new explicit Markov coupling for SDEs driven by multiplicative pure jump Lévy noises, which has been open for a long time in this area.

Keywords: Stochastic differential equation; Multiplicative pure jump Lévy noises; Coupling; Gradient estimate; Ergodicity (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (4)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:130:y:2020:i:5:p:3053-3094

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DOI: 10.1016/j.spa.2019.09.001

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