Periodic Solutions for SDEs through Upper and Lower Solutions

Abstract

We study a kind of better recurrence than Kolmogorov's one: periodicity recurrence,which corresponds periodic solutions in distribution for stochastic differential equations. On the basis of technique of upper and lower solutions and comparison principle, we obtain the existence of periodic solutions in distribution for stochastic differential equations (SDEs). Hence this provides an effective method how to study the periodicity of stochastic systems by analyzing deterministic ones. We also illustrate our results.

References in corpus (4)

• Random Periodic Solutions of Random Dynamical Systems
• Pathwise Random Periodic Solutions of Stochastic Differential Equations
• Persistence of periodic solutions for higher order perturbed differential systems via Lyapunov-Schmidt reduction
• Counterexamples to mean square almost periodicity of the solutions of some SDEs with almost periodic coefficients