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Fundam. Prikl. Mat., 2015, Volume 20, Issue 3, Pages 213–249 (Mi fpm1660)  

This article is cited in 1 scientific paper (total in 1 paper)

Reduction and integrability of stochastic dynamical systems

Nguyen Tien Zung, Nguyen Thanh Thien

Université Fédérale Toulouse Midi-Pyrénées, France

Abstract: This paper is devoted to the study of qualitative geometrical properties of stochastic dynamical systems, namely their symmetries, reduction, and integrability. In particular, we show that an SDS that is diffusion-wise symmetric with respect to a proper Lie group action can be diffusion-wise reduced to an SDS on the quotient space. We also show necessary and sufficient conditions for an SDS to be projectable via a surjective map. We then introduce the notion of integrability of SDS's, and extend the results about the existence and structure-preserving property of Liouville torus actions from the classical case to the case of integrable SDS's. We also show how integrable SDS's are related to compatible families of integrable Riemannian metrics on manifolds.

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English version:
Journal of Mathematical Sciences (New York), 2017, 225:4, 681–706

Bibliographic databases:

UDC: 519.216.73

Citation: Nguyen Tien Zung, Nguyen Thanh Thien, “Reduction and integrability of stochastic dynamical systems”, Fundam. Prikl. Mat., 20:3 (2015), 213–249; J. Math. Sci., 225:4 (2017), 681–706

Citation in format AMSBIB
\Bibitem{NguNgu15}
\by Nguyen~Tien~Zung, Nguyen~Thanh~Thien
\paper Reduction and integrability of stochastic dynamical systems
\jour Fundam. Prikl. Mat.
\yr 2015
\vol 20
\issue 3
\pages 213--249
\mathnet{http://mi.mathnet.ru/fpm1660}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3519755}
\elib{http://elibrary.ru/item.asp?id=32034515}
\transl
\jour J. Math. Sci.
\yr 2017
\vol 225
\issue 4
\pages 681--706
\crossref{https://doi.org/10.1007/s10958-017-3486-1}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Nguyen Tien Zung, “A conceptual approach to the problem of action-angle variables”, Arch. Ration. Mech. Anal., 229:2 (2018), 789–833  crossref  mathscinet  zmath  isi  scopus
  • Фундаментальная и прикладная математика
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