Stochastic viscosity solutions for SPDEs with continuous coefficients

Boualem Djehiche; Modeste N'zi; Jean Marc Owo

doi:10.1016/j.jmaa.2010.08.005

Stochastic viscosity solutions for SPDEs with continuous coefficients

Boualem Djehiche, Modeste N'zi, Jean Marc Owo

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

In this note, nonlinear stochastic partial differential equations (SPDEs) with continuous coefficients are studied. Via the solutions of backward doubly stochastic differential equations (BDSDEs) with continuous coefficients, we provide an existence result of stochastic viscosity sub- and super-solutions to this class of SPDEs. Under some stronger conditions, we prove the existence of stochastic viscosity solutions.

Original language	English (US)
Pages (from-to)	63-69
Number of pages	7
Journal	Journal of Mathematical Analysis and Applications
Volume	384
Issue number	1
DOIs	https://doi.org/10.1016/j.jmaa.2010.08.005
State	Published - Dec 1 2011

Keywords

Backward doubly stochastic differential equation
Stochastic partial differential equation
Stochastic viscosity solution

ASJC Scopus subject areas

Analysis
Applied Mathematics

Access to Document

10.1016/j.jmaa.2010.08.005

Cite this

@article{2784c7ef7e6c4b29a9bd1bb1cf9a8023,

title = "Stochastic viscosity solutions for SPDEs with continuous coefficients",

abstract = "In this note, nonlinear stochastic partial differential equations (SPDEs) with continuous coefficients are studied. Via the solutions of backward doubly stochastic differential equations (BDSDEs) with continuous coefficients, we provide an existence result of stochastic viscosity sub- and super-solutions to this class of SPDEs. Under some stronger conditions, we prove the existence of stochastic viscosity solutions.",

keywords = "Backward doubly stochastic differential equation, Stochastic partial differential equation, Stochastic viscosity solution",

author = "Boualem Djehiche and Modeste N'zi and Owo, {Jean Marc}",

year = "2011",

month = dec,

day = "1",

doi = "10.1016/j.jmaa.2010.08.005",

language = "English (US)",

volume = "384",

pages = "63--69",

journal = "Journal of Mathematical Analysis and Applications",

issn = "0022-247X",

publisher = "Academic Press Inc.",

number = "1",

}

TY - JOUR

T1 - Stochastic viscosity solutions for SPDEs with continuous coefficients

AU - Djehiche, Boualem

AU - N'zi, Modeste

AU - Owo, Jean Marc

PY - 2011/12/1

Y1 - 2011/12/1

N2 - In this note, nonlinear stochastic partial differential equations (SPDEs) with continuous coefficients are studied. Via the solutions of backward doubly stochastic differential equations (BDSDEs) with continuous coefficients, we provide an existence result of stochastic viscosity sub- and super-solutions to this class of SPDEs. Under some stronger conditions, we prove the existence of stochastic viscosity solutions.

AB - In this note, nonlinear stochastic partial differential equations (SPDEs) with continuous coefficients are studied. Via the solutions of backward doubly stochastic differential equations (BDSDEs) with continuous coefficients, we provide an existence result of stochastic viscosity sub- and super-solutions to this class of SPDEs. Under some stronger conditions, we prove the existence of stochastic viscosity solutions.

KW - Backward doubly stochastic differential equation

KW - Stochastic partial differential equation

KW - Stochastic viscosity solution

UR - http://www.scopus.com/inward/record.url?scp=79960845982&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=79960845982&partnerID=8YFLogxK

U2 - 10.1016/j.jmaa.2010.08.005

DO - 10.1016/j.jmaa.2010.08.005

M3 - Article

AN - SCOPUS:79960845982

SN - 0022-247X

VL - 384

SP - 63

EP - 69

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

IS - 1

ER -

Stochastic viscosity solutions for SPDEs with continuous coefficients

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this