Forward-backward doubly stochastic differential equations with Poisson jumps in infinite dimensions

TL;DR

This paper investigates the existence and uniqueness of solutions for a complex class of coupled stochastic differential equations with jumps in infinite-dimensional spaces, expanding the theoretical understanding of such systems.

Contribution

It introduces a novel approach to solving fully coupled forward-backward stochastic differential equations with Poisson jumps in infinite dimensions.

Findings

Proves existence and uniqueness of solutions.

Develops a method based on time continuation.

Extends stochastic differential equations theory to infinite dimensions.

Abstract

In this paper, we study the existence and uniqueness of solution to a system of nonlinear fully coupled forward-backward doubly stochastic differential equations with Poisson jumps. Our work is established in infinite dimensional separable Hilbert spaces and is based on the method of time continuation.