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Teor. Veroyatnost. i Primenen., 2003, Volume 48, Issue 1, Pages 22–42 (Mi tvp299)  

This article is cited in 2 scientific papers (total in 2 papers)

Parabolic Itô equations with nonsmooth nonlinearity and duality approach

N. G. Dokuchaev

St. Petersburg State University, Research Institute of Mathematics and Mechanics

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.

DOI: https://doi.org/10.4213/tvp299

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English version:
Theory of Probability and its Applications, 2004, 48:1, 45–62

Bibliographic databases:

Received: 16.08.1999
Revised: 02.10.2000

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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\by N.~G.~Dokuchaev
\paper Parabolic It\^o equations with nonsmooth nonlinearity and duality approach
\jour Teor. Veroyatnost. i Primenen.
\yr 2003
\vol 48
\issue 1
\pages 22--42
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\crossref{https://doi.org/10.4213/tvp299}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2013403}
\zmath{https://zbmath.org/?q=an:1064.60150}
\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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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Dokuchaev N., “Parabolic Ito equations with mixed in time conditions”, Stochastic Analysis and Applications, 26:3 (2008), 562–576  crossref  mathscinet  zmath  isi  scopus
    2. Dokuchaev N., “Representation of functionals of Ito processes and their first exit times”, Stochastics-An International Journal of Probability and Stochastic Processes, 83:1 (2011), 45–66  crossref  mathscinet  zmath  isi  scopus
  • Теория вероятностей и ее применения Theory of Probability and its Applications
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