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Izv. Akad. Nauk SSSR Ser. Mat., 1983, Volume 47, Issue 1, Pages 189–196 (Mi izv1384)  

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

On stochastic equations with degenerate diffusion with respect to some of the variables

A. Yu. Veretennikov


Abstract: In this paper the author establishes sufficient existence and uniqueness conditions for a strong solution of Itǒ's stochastic equation with nonsmooth drift under conditions of possible degeneracy of the diffusion with respect to some of the variables. The conditions thus found assume additional smoothness of the coefficients in the direction of the degeneracy.
Bibliography: 13 titles.

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English version:
Mathematics of the USSR-Izvestiya, 1984, 22:1, 173–180

Bibliographic databases:

UDC: 517.9
MSC: 60H10, 60J60
Received: 25.11.1981

Citation: A. Yu. Veretennikov, “On stochastic equations with degenerate diffusion with respect to some of the variables”, Izv. Akad. Nauk SSSR Ser. Mat., 47:1 (1983), 189–196; Math. USSR-Izv., 22:1 (1984), 173–180

Citation in format AMSBIB
\Bibitem{Ver83}
\by A.~Yu.~Veretennikov
\paper On stochastic equations with degenerate diffusion with respect to some of the variables
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1983
\vol 47
\issue 1
\pages 189--196
\mathnet{http://mi.mathnet.ru/izv1384}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=688921}
\zmath{https://zbmath.org/?q=an:0532.60052|0514.60056}
\transl
\jour Math. USSR-Izv.
\yr 1984
\vol 22
\issue 1
\pages 173--180
\crossref{https://doi.org/10.1070/IM1984v022n01ABEH001436}


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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. A. Yu. Veretennikov, “On the averaging principle for systems of stochastic differential equations”, Math. USSR-Sb., 69:1 (1991), 271–284  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    2. Levakov A.A., “Issledovanie ustoichivosti stokhasticheskikh differentsialnykh uravnenii s pomoschyu znakopostoyannykh funktsii lyapunova”, Differentsialnye uravneniya, 47:9 (2011), 1258–1267  elib
    3. Vaskovskii M.M., “Suschestvovanie $\beta$-martingalnykh reshenii stokhasticheskikh evolyutsionnykh funktsionalnykh uravnenii parabolicheskogo tipa s izmerimymi lokalno ogranichennymi koeffitsientami”, Differentsialnye uravneniya, 48:8 (2012), 1080–1080  elib
    4. Gunther Leobacher, Michaela Szölgyenyi, “A numerical method for SDEs with discontinuous drift”, Bit Numer Math, 2015  crossref
    5. A. Yu. Veretennikov, “On weak solutions of highly degenerate SDEs”, Autom. Remote Control, 81:3 (2020), 398–410  mathnet  crossref  crossref  isi  elib
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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