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Teoriya Veroyatnostei i ee Primeneniya, 2003, Volume 48, Issue 1, Pages 22–42
DOI: https://doi.org/10.4213/tvp299 (Mi tvp299) 		 
This article is cited in 4 scientific papers (total in 4 papers)

Parabolic Itô equations with nonsmooth nonlinearity and duality approach

N. G. Dokuchaev

St. Petersburg State University, Research Institute of Mathematics and Mechanics
Full-text PDF (1755 kB) Citations (4)
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DOI: https://doi.org/10.4213/tvp299
Abstract: This paper studies nonlinear stochastic partial differential equations with nonsmooth maximum type nonlinearity. The original equation is studied together with its adjoint equation being a backward stochastic parabolic equation, and together with an auxiliary optimal control problem. Conditions of solvability and uniqueness are obtained. In addition, it is shown that the solution is nonnegative if the free term is nonnegative.
Keywords: parabolic Itô equations, backward equations, stochastic control problems.
Received: 16.08.1999
Revised: 02.10.2000
English version:
Theory of Probability and its Applications, 2004, Volume 48, Issue 1, Pages 45–62
DOI: https://doi.org/10.1137/S0040585X980270
Bibliographic databases:
Language: Russian
Citation: N. G. Dokuchaev, “Parabolic Itô equations with nonsmooth nonlinearity and duality approach”, Teor. Veroyatnost. i Primenen., 48:1 (2003), 22–42; Theory Probab. Appl., 48:1 (2004), 45–62
Citation in format AMSBIB
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\paper Parabolic It\^o equations with nonsmooth nonlinearity and duality approach
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\pages 22--42
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\transl
\jour Theory Probab. Appl.
\yr 2004
\vol 48
\issue 1
\pages 45--62
\crossref{https://doi.org/10.1137/S0040585X980270}
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  • https://www.mathnet.ru/eng/tvp299
  • https://doi.org/10.4213/tvp299
  • https://www.mathnet.ru/eng/tvp/v48/i1/p22
    • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Теория вероятностей и ее применения Theory of Probability and its Applications
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