Backward stochastic dynamics with a subdifferential operator and non-local parabolic variational inequalities

Alain Bensoussan; Yiqun Li; Sheung Chi Phillip Yam

doi:10.1016/j.spa.2017.06.005

Backward stochastic dynamics with a subdifferential operator and non-local parabolic variational inequalities

Alain Bensoussan^*, Yiqun Li, Sheung Chi Phillip Yam

^*Corresponding author for this work

Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review

6 Citations (Scopus)

Abstract

In this article, we provide the first systematic study on the unique existence of the solution of backward stochastic dynamical variational inequalities on a general complete filtered probability space. We also build up a comprehensive analysis of the correspondence between these stochastic variational inequalities (resp. backward stochastic dynamics) and the weak solutions (instead of viscosity ones due to the intrinsic non-local nature of the integral of the gradient involved) of a class of non-local parabolic variational inequalities (resp. parabolic partial differential equations), which is barely touched in the existing literature due to its unconventional setting.

Original language	English
Pages (from-to)	644-688
Journal	Stochastic Processes and their Applications
Volume	128
Issue number	2
Online published	29 Jun 2017
DOIs	https://doi.org/10.1016/j.spa.2017.06.005
Publication status	Published - Feb 2018

Research Keywords

Backward stochastic dynamical variational inequalities
Integral of gradient
Non-local parabolic partial differential equations
Non-local parabolic variational inequalities
Norm equivalence
Penalized approach
Weak solutions

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RGC-funded

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@article{75ed05ea7deb4eaaab945ec81147f9cd,

title = "Backward stochastic dynamics with a subdifferential operator and non-local parabolic variational inequalities",

abstract = "In this article, we provide the first systematic study on the unique existence of the solution of backward stochastic dynamical variational inequalities on a general complete filtered probability space. We also build up a comprehensive analysis of the correspondence between these stochastic variational inequalities (resp. backward stochastic dynamics) and the weak solutions (instead of viscosity ones due to the intrinsic non-local nature of the integral of the gradient involved) of a class of non-local parabolic variational inequalities (resp. parabolic partial differential equations), which is barely touched in the existing literature due to its unconventional setting.",

keywords = "Backward stochastic dynamical variational inequalities, Integral of gradient, Non-local parabolic partial differential equations, Non-local parabolic variational inequalities, Norm equivalence, Penalized approach, Weak solutions",

author = "Alain Bensoussan and Yiqun Li and Yam, {Sheung Chi Phillip}",

year = "2018",

month = feb,

doi = "10.1016/j.spa.2017.06.005",

language = "English",

volume = "128",

pages = "644--688",

journal = "Stochastic Processes and their Applications",

issn = "0304-4149",

publisher = "Elsevier B.V.",

number = "2",

}

TY - JOUR

T1 - Backward stochastic dynamics with a subdifferential operator and non-local parabolic variational inequalities

AU - Bensoussan, Alain

AU - Li, Yiqun

AU - Yam, Sheung Chi Phillip

PY - 2018/2

Y1 - 2018/2

N2 - In this article, we provide the first systematic study on the unique existence of the solution of backward stochastic dynamical variational inequalities on a general complete filtered probability space. We also build up a comprehensive analysis of the correspondence between these stochastic variational inequalities (resp. backward stochastic dynamics) and the weak solutions (instead of viscosity ones due to the intrinsic non-local nature of the integral of the gradient involved) of a class of non-local parabolic variational inequalities (resp. parabolic partial differential equations), which is barely touched in the existing literature due to its unconventional setting.

AB - In this article, we provide the first systematic study on the unique existence of the solution of backward stochastic dynamical variational inequalities on a general complete filtered probability space. We also build up a comprehensive analysis of the correspondence between these stochastic variational inequalities (resp. backward stochastic dynamics) and the weak solutions (instead of viscosity ones due to the intrinsic non-local nature of the integral of the gradient involved) of a class of non-local parabolic variational inequalities (resp. parabolic partial differential equations), which is barely touched in the existing literature due to its unconventional setting.

KW - Backward stochastic dynamical variational inequalities

KW - Integral of gradient

KW - Non-local parabolic partial differential equations

KW - Non-local parabolic variational inequalities

KW - Norm equivalence

KW - Penalized approach

KW - Weak solutions

UR - http://www.scopus.com/inward/record.url?scp=85026304851&partnerID=8YFLogxK

UR - https://www.scopus.com/record/pubmetrics.uri?eid=2-s2.0-85026304851&origin=recordpage

U2 - 10.1016/j.spa.2017.06.005

DO - 10.1016/j.spa.2017.06.005

M3 - RGC 21 - Publication in refereed journal

SN - 0304-4149

VL - 128

SP - 644

EP - 688

JO - Stochastic Processes and their Applications

JF - Stochastic Processes and their Applications

IS - 2

ER -

Backward stochastic dynamics with a subdifferential operator and non-local parabolic variational inequalities

Abstract

Research Keywords

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GRF: Mean Field Control with Partial Information

GRF: Mean Field Theory, Stochastic Control and Systems of Partial Differential Equations

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Backward stochastic dynamics with a subdifferential operator and non-local parabolic variational inequalities

Abstract

Research Keywords

RGC Funding Information

Access Output

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GRF: Mean Field Control with Partial Information

GRF: Mean Field Theory, Stochastic Control and Systems of Partial Differential Equations

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