Numerical approximations of coupled forward-backward SPDEs with applications
type: CreativeWork
description: We introduce a new scheme combining the finite element method and machine learning techniques for the numerical approximations of coupled forward-backward stochastic partial differential equations (FBSPDEs) with homogeneous Dirichlet boundary conditions. For the FBSPDE, the finite element method in the spatial domain leads to approximations by finite-dimensional forward-backward stochastic differential equations (FBSDEs) in the temporal domain. We then approximate the solution of FBSDE by some existing machine learning schemes. Strong convergence results for spatial discretization of FBSPDEs are addressed.
abstract: We introduce a new scheme combining the finite element method and machine learning techniques for the numerical approximations of coupled forward-backward stochastic partial differential equations (FBSPDEs) with homogeneous Dirichlet boundary conditions. For the FBSPDE, the finite element method in the spatial domain leads to approximations by finite-dimensional forward-backward stochastic differential equations (FBSDEs) in the temporal domain. We then approximate the solution of FBSDE by some existing machine learning schemes. Strong convergence results for spatial discretization of FBSPDEs are addressed.
author: Molla, Md Hasib Uddin
language: eng
keywords: Stochastic partial differential equations, deep learning
date published: 2020-09-10
date modified: 2026-07-24T01:30:13Z
provider: University of Calgary
publisher: Networked Digital Library of Theses and Dissertations
type: WebPage
source organization: Science

PropertyValue
property ID: Handle
value: http://hdl.handle.net/1880/112515

PropertyValue
property ID: DOI
value: 10.11575/PRISM/38185