Existence of Periodic and Stationary Solutions to Distribution-Dependent SDEs

2025/01/15 by Wei Sun, Sun, Wei, Wong, Ethan
Economics, Econometrics and Finance · Engineering · #37A50 #60H10 #Economic theories and models #FOS: Mathematics #Probability (math.PR) #Process Optimization and Integration

paper · pdf · doi:10.48550/arxiv.2501.09176

openalex publication_date 2025/01/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We investigate the periodic and stationary solutions of distribution-dependent stochastic differential equations. While generally, the semigroups associated with the equations are nonlinear, we show that the methods of weak convergence and Lyapunov functions can be combined to give efficient criteria for the existence of periodic and stationary solutions. Concrete examples are presented to illustrate the novel criteria.

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