RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PERSONAL OFFICE
General information
Latest issue
Forthcoming papers
Archive
Impact factor
Subscription
Guidelines for authors
License agreement
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Mat. Sb.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Mat. Sb. (N.S.), 1988, Volume 136(178), Number 4(8), Pages 510–529 (Mi msb1757)  

This article is cited in 4 scientific papers (total in 4 papers)

On moment estimates for quasiderivative of solutions of stochastic equations with respect to the initial data, and their applications

N. V. Krylov


Abstract: There is a well-known method for proving smoothness of a probabilistic solution of an elliptic equation in space, based on studying the growth as $t\to\infty$ of the moments of the derivatives with respect to the initial data of a solution of an Ito stochastic equation. This article introduces the concept of quasiderivatives, which “work” in the places where derivatives work, and which enable one to essentially weaken the known conditions ensuring smoothness of a probabilistic solution of an elliptic equation.
Bibliography: 12 titles.

Full text: PDF file (1115 kB)
References: PDF file   HTML file

English version:
Mathematics of the USSR-Sbornik, 1989, 64:2, 505–526

Bibliographic databases:

UDC: 517.95
MSC: 60H10, 60H15
Received: 25.02.1987

Citation: N. V. Krylov, “On moment estimates for quasiderivative of solutions of stochastic equations with respect to the initial data, and their applications”, Mat. Sb. (N.S.), 136(178):4(8) (1988), 510–529; Math. USSR-Sb., 64:2 (1989), 505–526

Citation in format AMSBIB
\Bibitem{Kry88}
\by N.~V.~Krylov
\paper On moment estimates for quasiderivative of solutions of stochastic equations with respect to the initial data, and their applications
\jour Mat. Sb. (N.S.)
\yr 1988
\vol 136(178)
\issue 4(8)
\pages 510--529
\mathnet{http://mi.mathnet.ru/msb1757}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=965890}
\zmath{https://zbmath.org/?q=an:0677.60064|0658.60086}
\transl
\jour Math. USSR-Sb.
\yr 1989
\vol 64
\issue 2
\pages 505--526
\crossref{https://doi.org/10.1070/SM1989v064n02ABEH003323}


Linking options:
  • http://mi.mathnet.ru/eng/msb1757
  • http://mi.mathnet.ru/eng/msb/v178/i4/p510

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    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. N. V. Krylov, “On control of diffusion processes on a surface in Euclidean space”, Math. USSR-Sb., 65:1 (1990), 185–203  mathnet  crossref  mathscinet  zmath
    2. N. V. Krylov, “Smoothness of the value function for a controlled diffusion process in a domain”, Math. USSR-Izv., 34:1 (1990), 65–95  mathnet  crossref  mathscinet  zmath
    3. N. V. Krylov, “On the first quasiderivatives of solutions of Ito stochastic equations”, Russian Acad. Sci. Izv. Math., 40:2 (1993), 377–403  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    4. Zhou W., “The Quasiderivative Method for Derivative Estimates of Solutions to Degenerate Elliptic Equations”, Stoch. Process. Their Appl., 123:8 (2013), 3064–3099  crossref  isi
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
    Number of views:
    This page:197
    Full text:53
    References:31

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2019