WELL-POSEDNESS, STABILITY AND SENSITIVITIES FOR STOCHASTIC DELAY EQUATIONS: A GENERALIZED COUPLING APPROACH

• 成果类型: Article
• 署名作者: Kulik, Alexei; Scheutzow, Michael
• 署名单位: Wroclaw University of Science & Technology; Technical University of Berlin
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/20-AOP1449
• 发表日期: 2020
• 页码: 3041-3076
• 关键词: subgeometric rates; harnack inequality; Markov; approximation; CONVERGENCE; ergodicity

摘要

We develop a new generalized coupling approach to the study of stochastic delay equations with Holder continuous coefficients, for which analytical PDE-based methods are not available. We prove that such equations possess unique weak solutions, and establish weak ergodic rates for the corresponding segment processes. We also prove, under additional smoothness assumptions on the coefficients, stabilization rates for the sensitivities in the initial value of the corresponding semigroups.