Ergodicity of stochastic differential equations with jumps and singular coefficients

2017/05/21 by Longjie Xie, Xicheng Zhang, Xie, Longjie +1 · 5 citations
Economics, Econometrics and Finance · Mathematics · #60H10 #60J60 #Credit Risk and Financial Regulations #FOS: Mathematics #Probability (math.PR) #Statistical Methods and Inference #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.1705.07402

openalex publication_date 2017/05/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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