Regularity preservation in Kolmogorov equations for non-Lipschitz coefficients under Lyapunov conditions

• 成果类型: Article
• 署名作者: Chak, Martin
• 署名单位: Sorbonne Universite; Universite Paris Cite
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-024-01313-0
• 发表日期: 2024
• 页码: 259-319
• 关键词: STOCHASTIC DIFFERENTIAL-EQUATIONS; Markovian processes; strong completeness; CONVERGENCE; STABILITY; time; schemes; rates; sdes

摘要

Given global Lipschitz continuity and differentiability of high enough order on the coefficients in It & ocirc;'s equation, differentiability of associated semigroups, existence of twice differentiable solutions to Kolmogorov equations and weak convergence rates of order one for numerical approximations are known. In this work and against the counterexamples of Hairer et al. (Ann Probab 43(2):468-527, https://doi.org/10.1214/13-AOP838, 2015), the drift and diffusion coefficients having Lipschitz constants that are o(logV) and o(root log V) respectively for a function V satisfying (partial derivative(t)+L)V <= CV is shown to be a generalizing condition in place of global Lipschitz continuity for the above.