A Modified log-Harnack inequality and asymptotically strong Feller property

2011/02/06 by Lihu Xu, Xu, Lihu · 1 citation
Economics, Econometrics and Finance · Engineering · Mathematics · #60J45 #60J75 #FOS: Mathematics #Fluid Dynamics and Turbulent Flows #Geometric Analysis and Curvature Flows #Probability (math.PR) #Stochastic processes and financial applications #math.PR #msc:60J45 #msc:60J75

paper · pdf · doi:10.48550/arxiv.1102.1162

18 pages

arxiv created 2011/02/06 · openalex publication_date 2011/02/06 · arxiv updated 2011/02/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We introduce a new functional inequality, which is a modification of log-Harnack inequality established in [20] and [29], and prove that it implies the asymptotically strong Feller property (ASF). This inequality seems to generalize the criterion for ASF in [Proposition 3.12,14]. As a example, we show by an asymptotic coupling that 2D stochastic Navier-Stokes equation driven by highly degenerate but essentially elliptic noises satisfies our modified log-Harnack inequality.

Citations

• An Introduction to Stochastic PDEs
• A Theory of Hypoellipticity and Unique Ergodicity for Semilinear Stochastic PDEs

Cited by

• Asymptotic log-Harnack inequality for path-distribution dependent SDEs with infinite memory and Dini drift

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