Well-posedness of Backward Stochastic Partial Differential Equations with Lyapunov Condition

TL;DR

This paper establishes the existence and uniqueness of strong solutions for a broad class of backward stochastic partial differential equations under Lyapunov and local monotonicity conditions, expanding the theoretical framework beyond classical assumptions.

Contribution

It introduces a generalized variational approach using Lyapunov and local monotonicity conditions, enabling analysis of more general BSPDE models.

Findings

Proves existence and uniqueness of solutions under new conditions.

Extends applicability to quasilinear and semilinear BSPDEs.

Provides a generalized variational framework.

Abstract

In this paper we show the existence and uniqueness of strong solutions for a large class of backward SPDE where the coefficients satisfy a specific type Lyapunov condition instead of the classical coercivity condition. Moreover, based on the generalized variational framework, we also use the local monotonicity condition to replace the standard monotonicity condition, which is applicable to various quasilinear and semilinear BSPDE models.