Backward Doubly Stochastic Equations with Jumps and Comparison Theorems

TL;DR

This paper establishes existence, uniqueness, and comparison theorems for backward doubly stochastic differential equations with jumps, advancing theoretical understanding and providing tools for solving complex stochastic systems.

Contribution

It introduces new existence and uniqueness results for backward doubly stochastic equations with jumps and develops comparison theorems under weak conditions.

Findings

Proved existence and pathwise uniqueness of solutions.

Established comparison theorems for these equations.

Applied comparison theorems to specific equations with linear drift.

Abstract

In this work we mainly prove the existence and pathwise uniqueness of solutions to general backward doubly stochastic differential equations with jumps appearing in both forward and backward integral parts. Several comparison theorems under some weak conditions are also given. Finally we apply comparison theorems in proving the existence of solution to some special backward doubly stochastic differential equations with drift coefficient increasing linearly.