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

TL;DR

This paper investigates linear backward stochastic PDEs with unique boundary conditions linking the terminal value to the entire past solution, establishing key results on their uniqueness, solvability, and regularity.

Contribution

It introduces a novel class of backward SPDEs with non-local boundary conditions in time and space, providing foundational theoretical results.

Findings

Proved uniqueness of solutions

Established solvability conditions

Analyzed regularity properties

Abstract

We study linear backward stochastic partial differential equations of parabolic type with special boundary condition that connect the terminal value of the solution with a functional over the entire past solution. Uniqueness, solvability and regularity results for the solutions are obtained.