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Teor. Veroyatnost. i Primenen., 2016, Volume 61, Issue 2, Pages 268–299 (Mi tvp5056)  

This article is cited in 5 scientific papers (total in 6 papers)

Stochastic interpretation of quasilinear parabolic systems with cross-diffusion

Ya. I. Belopol'skaya

St. Petersburg State University of Architecture and Civil Engineering

Abstract: We construct a stochastic interpretation of the generalized solution of the Cauchy problem for a strongly coupled system of quasilinear parabolic equations. To this end we derive a system of stochastic equations and prove that its solution allows us to construct a probabilistic representation of the original Cauchy problem solution and investigate its properties. Our construction of a probabilistic representation of the generalized solution of the Cauchy problem is crucially based on results of stochastic flow theory.

Funding Agency Grant Number
Russian Foundation for Basic Research 15-01-01453_а


DOI: https://doi.org/10.4213/tvp5056

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English version:
Theory of Probability and its Applications, 2017, 61:2, 208–234

Bibliographic databases:

Received: 23.04.2015

Citation: Ya. I. Belopol'skaya, “Stochastic interpretation of quasilinear parabolic systems with cross-diffusion”, Teor. Veroyatnost. i Primenen., 61:2 (2016), 268–299; Theory Probab. Appl., 61:2 (2017), 208–234

Citation in format AMSBIB
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\by Ya.~I.~Belopol'skaya
\paper Stochastic interpretation of quasilinear parabolic systems with cross-diffusion
\jour Teor. Veroyatnost. i Primenen.
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\issue 2
\pages 268--299
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\transl
\jour Theory Probab. Appl.
\yr 2017
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\issue 2
\pages 208--234
\crossref{https://doi.org/10.1137/S0040585X97T988113}
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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. “International conference on stochastic methods (Abstracts)”, Theory Probab. Appl., 62:4 (2018), 640–674  mathnet  crossref  crossref  isi  elib
    2. Ya. I. Belopolskaya, A. O. Stepanova, “Stokhasticheskaya interpretatsiya sistemy MGD–Byurgers”, Veroyatnost i statistika. 26, Zap. nauchn. sem. POMI, 466, POMI, SPb., 2017, 7–29  mathnet
    3. Ya. I. Belopolskaya, “Stokhasticheskie modeli protsessov khemotaksisa”, Veroyatnost i statistika. 27, Zap. nauchn. sem. POMI, 474, POMI, SPb., 2018, 7–27  mathnet
    4. Ya. Belopolskaya, “Stochastic models for forward systems of nonlinear parabolic equations”, Statist. Papers, 59:4 (2018), 1505–1519  crossref  mathscinet  zmath  isi  scopus
    5. “Abstracts of talks given at the 3rd International Conference on Stochastic Methods”, Theory Probab. Appl., 64:1 (2019), 124–169  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    6. “Abstracts of talks given at the 4th International Conference on Stochastic Methods”, Theory Probab. Appl., 65:1 (2020), 121–172  mathnet  crossref  crossref  isi  elib
  • Теория вероятностей и ее применения Theory of Probability and its Applications
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