Work

Averaging principles for forward-backward multivalued stochastic systems and applications to systems of nonlinear parabolic partial differential equations

Year: 2025

Type: article

Abstract: This work concerns a type of stochastic systems in which the forward equations are general stochastic differential equations and the backward equations are stochastic variational inequalities. We first prove an averaging principle for general stochastic differential equations in the $L^{2p}$ ($p\geq 1$) sense. In addition, a convergence rate for $p=1$ is presented. Combining general stochastic differential equations with backward stochastic variational inequalities, we then establish another averaging principle for backward stochastic variational inequalities in the $L^{2}$ sense using a time discretization method. Finally, we apply our result to nonlinear parabolic partial differential equations to obtain their averaging principles.

Source: Probability Uncertainty and Quantitative Risk

DOI: 10.3934/puqr.2025009

Author: Huijie Qiao

Institution: Southeast University

Language: English

Topic: Stochastic processes and financial applications

Subfield: Finance

Field: Economics, Econometrics and Finance

Domain: Social Sciences

Open Access status: hybrid

Funder: National Natural Science Foundation of China

Award: 带跳随机偏微分方程若干性质研究