Mean-field forward-backward doubly stochastic differential equations and related nonlocal stochastic partial differential equations
type: Item
instance of: scholarly article
title: Mean-field forward-backward doubly stochastic differential equations and related nonlocal stochastic partial differential equations
zbMATH Open document ID: 1469.60200
DOI: 10.1155/2014/194341
published in: Abstract and Applied Analysis
publication date: 2019-02-14T00:00:00Z
review text: Summary: Mean-field forward-backward doubly stochastic differential equations (MF-FBDSDEs) are studied, which extend many important equations well studied before. Under some suitable monotonicity assumptions, the existence and uniqueness results for measurable solutions are established by means of a method of continuation. Furthermore, the probabilistic interpretation for the solutions to a class of nonlocal stochastic partial differential equations (SPDEs) combined with algebra equations is given.
Mathematics Subject Classification ID: 60H10
Mathematics Subject Classification ID: 60H15
zbMATH DE Number: 7021911
zbMATH Keywords: nonlocal stochastic partial differential equations
zbMATH Keywords: mean-field forward-backward doubly stochastic differential equations
author: Qingfeng Zhu
author: Yufeng Shi
Wikidata QID: Q59035949
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2014/194341
OpenAlex ID: W1968886571
cites work: Backward doubly stochastic differential equations and systems of quasilinear SPDEs
cites work: Weak solutions for SPDE's and backward doubly stochastic differential equations
cites work: Strong uniqueness for an SPDE via backward doubly stochastic differential equations
cites work: Stochastic PDIEs with nonlinear Neumann boundary conditions and generalized backward doubly stochastic differential equations driven by Lévy processes
cites work: Stochastic PDIEs and backward doubly stochastic differential equations driven by Lévy processes
cites work: Stationary solutions of SPDEs and infinite horizon BDSDEs
cites work: Stationary solutions of SPDEs and infinite horizon BDSDEs with non-Lipschitz coefficients
cites work: SPDEs with polynomial growth coefficients and the Malliavin calculus method
cites work: A type of time-symmetric forward-backward stochastic differential equations
cites work: Solutions to general forward-backward doubly stochastic differential equations
cites work: Forward-backward doubly stochastic differential equations and related stochastic partial differential equations
cites work: Maximum Principle for Backward Doubly Stochastic Control Systems with Applications
cites work: Maximum principle for forward-backward doubly stochastic control systems and applications
cites work: Partially observed optimal controls of forward-backward doubly stochastic systems
cites work: Q3236483
cites work: A CLASS OF MARKOV PROCESSES ASSOCIATED WITH NONLINEAR PARABOLIC EQUATIONS
cites work: Nonlinear Diffusion Governed by McKean–Vlasov Equation on Hilbert Space and Optimal Control
cites work: A semilinear McKean-Vlasov stochastic evolution equation in Hilbert space
cites work: McKean–Vlasov Limit in Portfolio Optimization
cites work: Dynamics of the McKean-Vlasov equation
cites work: Approximate McKean–Vlasov representations for a class of SPDEs
cites work: A class of quasilinear stochastic partial differential equations of McKean-Vlasov type with mass conservation
cites work: Macroscopic limits for stochastic partial differential equations of McKean-Vlasov type
cites work: Mean field games
cites work: Large population stochastic dynamic games: closed-loop McKean-Vlasov systems and the Nash certainty equivalence principle
cites work: Mean-field backward stochastic differential equations: A limit approach
cites work: Mean-field backward doubly stochastic differential equations and related SPDEs
cites work: Mean-field backward stochastic differential equations and related partial differential equations
cites work: Q5694163
cites work: Optimal Control Problems of Fully Coupled FBSDEs and Viscosity Solutions of Hamilton--Jacobi--Bellman Equations
cites work: Stochastic calculus with anticipating integrands
description: scientific article; zbMATH DE number 7021911