On Backward Doubly Stochastic Differential Evolutionary System

Abstract

In this paper, we are concerned with backward doubly stochastic differential evolutionary systems (BDSDESs for short). By using a variational approach based on the monotone operator theory, we prove the existence and uniqueness of the solutions for BDSDESs. We also establish an Itô formula for the Banach space-valued BDSDESs.

33 pages

References in corpus (2)

• SPDE in Hilbert Space with Locally Monotone Coefficients
• Stationary Solutions of SPDEs and Infinite Horizon BDSDEs

Cited by in corpus (3)

• Weak Solution for a Class of Fully Nonlinear Stochastic Hamilton-Jacobi-Bellman Equations
• A Constrained Control Problem with Degenerate Coefficients and Degenerate Backward SPDEs with Singular Terminal Condition
• Controlled Reflected SDEs and Neumann Problem for Backward SPDEs