2022/02/20 by Jianhai Bao, Yue Wu, Bao, Jianhai +1
Economics, Econometrics and Finance · Engineering · Social Sciences · #34K13 #34K50 #60H10 #Dynamical Systems (math.DS) #FOS: Mathematics #Insurance, Mortality, Demography, Risk Management #Probability (math.PR) #Stability and Controllability of Differential Equations #Stochastic processes and financial applications
paper · doi:10.48550/arxiv.2202.09771
openalex publication_date 2022/02/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper is concerned with the existence and uniqueness of random periodic solutions for stochastic differential equations (SDEs), where the drift terms involved need not to be uniformly dissipative. On the one hand, via the reflection coupling approach, we investigate the existence of random periodic solutions in the sense of distribution for SDEs without memory, where the drifts are merely dissipative at long distance. On the other hand, via the synchronous coupling strategy, we establish respectively the existence of pathwise random periodic solutions for functional SDEs with a finite time lag and an infinite time lag, in which the drifts are only dissipative on average rather than uniformly dissipative with respect to the time parameters.