Backward stochastic differential equations (BSDES) using infinite-dimensional martingales with subdifferential operator
Document Type
Article
Publication Date
10-1-2022
Abstract
In this paper, we focus on a family of backward stochastic differential equations (BSDEs) with subdifferential operators that are driven by infinite-dimensional martingales. We shall show that the solution to such infinite-dimensional BSDEs exists and is unique. The existence and uniqueness of the solution are established using Yosida approximations. Furthermore, as an application of the main result, we shall show that the backward stochastic partial differential equation driven by infinite-dimensional martingales with a continuous linear operator has a unique solution under the special condition that the F-t-progressively measurable generator F of the model we proposed in this paper equals zero.
Keywords
Backward stochastic differential equations (BSDEs), Variational inequalities, Martingales, Subdifferential operators
Divisions
Science
Funders
Anhui Philosophy and Social Science Planning Project [AHSKQ2021D98],Universiti Malaya research project [BKS073-2017]
Publication Title
Axioms
Volume
11
Issue
10
Publisher
MDPI
Publisher Location
ST ALBAN-ANLAGE 66, CH-4052 BASEL, SWITZERLAND