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Izv. Akad. Nauk SSSR Ser. Mat., 1974, Volume 38, Issue 1, Pages 228–248 (Mi izv1899)  

This article is cited in 11 scientific papers (total in 11 papers)

Some estimates of the probability density of a stochastic integral

N. V. Krylov


Abstract: Estimates in $L_p$ are derived for probability densities of stochastic integrals. An example is presented which shows that for some values of $p$ such estimates are not attainable. The method of proving these estimates is based on a study of Bellman's nonlinear equations and the properties of $\lambda$-convex functions.

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English version:
Mathematics of the USSR-Izvestiya, 1974, 8:1, 233–254

Bibliographic databases:

UDC: 519.2
MSC: Primary 60H05; Secondary 60E05, 60H20, 60J25, 26A51
Received: 26.12.1972

Citation: N. V. Krylov, “Some estimates of the probability density of a stochastic integral”, Izv. Akad. Nauk SSSR Ser. Mat., 38:1 (1974), 228–248; Math. USSR-Izv., 8:1 (1974), 233–254

Citation in format AMSBIB
\Bibitem{Kry74}
\by N.~V.~Krylov
\paper Some estimates of the probability density of a~stochastic integral
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1974
\vol 38
\issue 1
\pages 228--248
\mathnet{http://mi.mathnet.ru/izv1899}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=345206}
\zmath{https://zbmath.org/?q=an:0293.60049}
\transl
\jour Math. USSR-Izv.
\yr 1974
\vol 8
\issue 1
\pages 233--254
\crossref{https://doi.org/10.1070/IM1974v008n01ABEH002103}


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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, N. V. Krylov, “On explicit formulas for solutions of stochastic equations”, Math. USSR-Sb., 29:2 (1976), 239–256  mathnet  crossref  mathscinet  zmath  isi
    2. N. V. Krylov, B. L. Rozovskii, “On conditional distributions of diffusion processes”, Math. USSR-Izv., 12:2 (1978), 336–356  mathnet  crossref  mathscinet  zmath
    3. S. V. Anulova, “On processes with Lévy generating operator in a half-space”, Math. USSR-Izv., 13:1 (1979), 9–51  mathnet  crossref  mathscinet  zmath  isi
    4. A. Yu. Veretennikov, “On strong solutions and explicit formulas for solutions of stochastic integral equations”, Math. USSR-Sb., 39:3 (1981), 387–403  mathnet  crossref  mathscinet  zmath  isi
    5. P. L. Lions, “On the Hamilton–Jacobi–Bellman equations”, Acta Appl Math, 1:1 (1983), 17  crossref  mathscinet  zmath  isi
    6. Nigel J. Cutland, “Simplified existence for solutions to stochastic differential equations”, Stochastics, 14:4 (1985), 319  crossref
    7. Nigel J. Cutland, “Infinitesimal methods in control theory: Deterministic and stochastic”, Acta Appl Math, 5:2 (1986), 105  crossref  mathscinet  zmath  isi
    8. N. V. Krylov, “On estimates of the maximum of a solution of a parabolic equation and estimates of the distribution of a semimartingale”, Math. USSR-Sb., 58:1 (1987), 207–221  mathnet  crossref  mathscinet  zmath
    9. R. Mikulevicius, B. Rozovskii, “Linear Parabolic Stochastic PDE and Wiener Chaos”, SIAM J Math Anal, 29:2 (1998), 452  crossref  mathscinet  zmath  isi
    10. N.V. Krylov, R. Liptser, “On diffusion approximation with discontinuous coefficients”, Stochastic Processes and their Applications, 102:2 (2002), 235  crossref
    11. Alexey Rudenko, “Some properties of the Itô–Wiener expansion of the solution of a stochastic differential equation and local times”, Stochastic Processes and their Applications, 2012  crossref
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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