On linear, degenerate backward stochastic partial differential equations

In this paper we study the well-posedness and regularity of the adapted solutions to a class of linear, degenerate backward stochastic partial differential equations (BSPDE, for short). We establish new a priori estimates for the adapted solutions to BSPDEs in a general setting, based on which the e...

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Published inProbability theory and related fields Vol. 113; no. 2; pp. 135 - 170
Main Authors Ma, Jin, Yong, Jiongmin
Format Journal Article
LanguageEnglish
Published Heidelberg Springer 01.02.1999
Berlin Springer Nature B.V
New York, NY
Subjects
Exact sciences and technology
Mathematical analysis
Mathematics
Partial differential equations
Probability
Probability and statistics
Probability theory and stochastic processes
Regularity
Sciences and techniques of general use
Stochastic analysis
Solution uniqueness
Stochastic analysis
Linear equation
Existence of solution
Finance
Solution regularity
A priori estimation
Well posed problem
Comparison theorem
Partial differential equation
Stochastic equation
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Summary:In this paper we study the well-posedness and regularity of the adapted solutions to a class of linear, degenerate backward stochastic partial differential equations (BSPDE, for short). We establish new a priori estimates for the adapted solutions to BSPDEs in a general setting, based on which the existence, uniqueness, and regularity of adapted solutions are obtained. Also, we prove some comparison theorems and discuss their possible applications in mathematical finance.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
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ISSN:0178-8051
1432-2064
DOI:10.1007/s004400050205