Ergodicity of stochastic differential equations with jumps and singular coefficients

Abstract

We show the strong well-posedness of SDEs driven by general multiplicative Lévy noises with Sobolev diffusion and jump coefficients and integrable drift. Moreover, we also study the strong Feller property, irreducibility as well as the exponential ergodicity of the corresponding semigroup when the coefficients are time-independent and singular dissipative. In particular, the large jump is allowed in the equation. To achieve our main results, we present a general approach for treating the SDEs with jumps and singular coefficients so that one just needs to focus on Krylov's {\it apriori} estimates for SDEs.

arXiv comment60pages

Cited by in corpus (13)

• Heat kernel and ergodicity of SDEs with distributional drifts
• Well-posedness of distribution dependent SDEs with singular drifts
• Strong and weak convergence in the averaging principle for SDEs with Hölder coefficients
• Gradient Estimates and Ergodicity for SDEs Driven by Multiplicative Lévy Noises via Coupling
• A Zvonkin's transformation for stochastic differential equations with singular drift and related applications
• Exponential convergence in Wasserstein Distance for Diffusion Semigroups with Irregular Drifts
• Distribution Dependent SDEs with Singular Coefficients
• SDEs with singular drifts and multiplicative noise on general space-time domains
• Periodic solutions of stochastic differential equations driven by Levy noises
• Well-posedness and long time behavior of singular Langevin stochastic differential equations
• Error estimates of the backward Euler-Maruyama method for multi-valued stochastic differential equations
• Well-posedness for SDEs driven by different type of noises
• Strong Uniqueness of Degenerate SDEs with Hölder diffusion coefficients