On almost surely periodic and almost periodic solutions of backward SPDEs

Abstract

We study linear backward stochastic partial differential equations of parabolic type with special boundary conditions in time. The standard Cauchy condition at the terminal time is replaced by a condition that holds almost surely and mixes the random values of the solution at different times, including the terminal time, initial time and continuously distributed times. Uniqueness, solvability and regularity results for the solutions are obtained. In particular, conditions of existence of periodic in time and "almost periodic" solutions are obtained for backward SPDEs.

arXiv comment23 pages. arXiv admin note: substantial text overlap with arXiv:1211.1460, arXiv:1211.5858

References in corpus (3)

• Random Periodic Solutions of SPDEs via Integral Equations and Wiener-Sobolev Compact Embedding
• Counterexamples to mean square almost periodicity of the solutions of some SDEs with almost periodic coefficients
• Backward SPDEs with non-local in time and space boundary conditions

Cited by in corpus (1)

• Backward SPDEs with non-local in time and space boundary conditions