Periodic solution of stochastic process in the distributional sense. (English) Zbl 1481.35418
Summary: In this paper, we aim to study a stochastic process from a macro point of view, and thus, periodic solution of a stochastic process in distributional sense is introduced. We first give the definition and then establish the existence of periodic solution on bounded domain. Lastly, for the case that probability density function exists, we obtain the existence periodic solutions of the probability density function corresponding to the stochastic process by using the technique of deterministic partial differential equations.
MSC:
| 35R60 | PDEs with randomness, stochastic partial differential equations |
| 35B10 | Periodic solutions to PDEs |
| 35K20 | Initial-boundary value problems for second-order parabolic equations |
| 35Q84 | Fokker-Planck equations |
| 60H15 | Stochastic partial differential equations (aspects of stochastic analysis) |
| 60H40 | White noise theory |
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