Comparison Theorem of Multi-dimensional Backward Doubly Stochastic Differential Equations on Infinite Horizon

TL;DR

This paper establishes a comparison theorem for multi-dimensional backward doubly stochastic differential equations on an infinite horizon under quasi-monotone conditions, providing theoretical insights and an illustrative example.

Contribution

It introduces a novel comparison theorem for multi-dimensional backward doubly stochastic differential equations on infinite horizons under quasi-monotone assumptions.

Findings

Established a comparison theorem for the equations.

Provided an example illustrating the theorem.

Extended the theory to infinite horizon cases.

Abstract

Under quasi-monotone assumptions for coefficients, we show one kind of comparison theorem for multi-dimensional\textbf{\}backward doubly stochastic differential equations on infinite horizon. An example is given as well.