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Foundations of the theory of semilinear stochastic partial differential equations
Foundations of the theory of semilinear stochastic partial differential equations
- Source :
- International Journal of Stochastic Analysis 2013 (2013), International Journal of Stochastic Analysis, Vol 2013 (2013)
- Publication Year :
- 2019
- Publisher :
- arXiv, 2019.
-
Abstract
- The goal of this review article is to provide a survey about the foundations of semilinear stochastic partial differential equations. In particular, we provide a detailed study of the concepts of strong, weak and mild solutions, establish their connections, and review a standard existence- and uniqueness result. The proof of the existence result is based on a slightly extended version of the Banach fixed point theorem.<br />Comment: 36 pages
- Subjects :
- Statistics and Probability
stochastic analysis
symbols.namesake
FOS: Mathematics
Applied mathematics
Uniqueness
ddc:510
C0-semigroup
Mathematics
60H15, 60G17
Banach fixed-point theorem
Stochastic process
lcsh:Mathematics
Applied Mathematics
Mathematical analysis
Probability (math.PR)
Hilbert space
lcsh:QA1-939
Hilbert Spaces
Dewey Decimal Classification::500 | Naturwissenschaften::510 | Mathematik
Functional Analysis (math.FA)
Mathematics - Functional Analysis
Stochastic partial differential equation
Modeling and Simulation
symbols
Semilinear stochastic partial differential equations (SPDEs)
Mathematics - Probability
Analysis
Numerical partial differential equations
Subjects
Details
- Database :
- OpenAIRE
- Journal :
- International Journal of Stochastic Analysis 2013 (2013), International Journal of Stochastic Analysis, Vol 2013 (2013)
- Accession number :
- edsair.doi.dedup.....231593b68d906fc6845fba90fc03a368
- Full Text :
- https://doi.org/10.48550/arxiv.1907.02352