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Izv. Akad. Nauk SSSR Ser. Mat., 1973, Volume 37, Issue 3, Pages 691–708 (Mi izv2287)  

This article is cited in 19 scientific papers (total in 19 papers)

On the selection of a Markov process from a system of processes and the construction of quasi-diffusion processes

N. V. Krylov


Abstract: In this paper the notion of a Markov system of processes is introduced, and it is proved that a Markov process can be selected from such a system. The usefulness of this fact is illustrated by the example of constructing quasidiffusion processes with “poor” coefficients (e.g. with a degenerate diffusion matrix).

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English version:
Mathematics of the USSR-Izvestiya, 1973, 7:3, 691–709

Bibliographic databases:

UDC: 519.2
MSC: Primary 60I25, 60I60; Secondary 93E20, 60H10
Received: 19.10.1971

Citation: N. V. Krylov, “On the selection of a Markov process from a system of processes and the construction of quasi-diffusion processes”, Izv. Akad. Nauk SSSR Ser. Mat., 37:3 (1973), 691–708; Math. USSR-Izv., 7:3 (1973), 691–709

Citation in format AMSBIB
\Bibitem{Kry73}
\by N.~V.~Krylov
\paper On the selection of a~Markov process from a~system of processes and the construction of quasi-diffusion processes
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1973
\vol 37
\issue 3
\pages 691--708
\mathnet{http://mi.mathnet.ru/izv2287}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=339338}
\zmath{https://zbmath.org/?q=an:0295.60057}
\transl
\jour Math. USSR-Izv.
\yr 1973
\vol 7
\issue 3
\pages 691--709
\crossref{https://doi.org/10.1070/IM1973v007n03ABEH001971}


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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. N. V. Krylov, “Some estimates of the probability density of a stochastic integral”, Math. USSR-Izv., 8:1 (1974), 233–254  mathnet  crossref  mathscinet  zmath
    2. R. A. Holley, D. W. Stroock, “Nearest neighbor birth and death processes on the real line”, Acta Math, 140:1 (1978), 103  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. S. V. Anulova, “On stochastic differential equations with boundary conditions in a half-plane”, Math. USSR-Izv., 18:3 (1982), 423–437  mathnet  crossref  mathscinet  zmath
    5. P. L. Lions, “On the Hamilton–Jacobi–Bellman equations”, Acta Appl Math, 1:1 (1983), 17  crossref  mathscinet  zmath  isi
    6. L. L. Helms, “Order properties of attractive spin systems”, Acta Appl Math, 2:3-4 (1984), 379  crossref  mathscinet  zmath  isi
    7. A. N. Kochubei, “Singular parabolic equations and Markov processes”, Math. USSR-Izv., 24:1 (1985), 73–97  mathnet  crossref  mathscinet  zmath
    8. N. V. Krylov, “An Approach to Controlled Diffusion Processes”, Theory Probab Appl, 31:4 (1987), 604  mathnet  crossref  mathscinet  isi
    9. Karoui Nicole el, Nguyen Du'hŪŪ, Jeanblanc-Picqué Monique, “Compactification methods in the control of degenerate diffusions: existence of an optimal control”, Stochastics, 20:3 (1987), 169  crossref
    10. N. V. Krylov, N. V. Krylov, “On One-Point Weak Uniqueness for Elliptic Equations”, Communications in Partial Differential Equations, 17:11-12 (1992), 405  crossref
    11. V.S. Borkar, T.E. Govindan, “Optimal control of semilinear stochastic evolution equations”, Nonlinear Analysis: Theory, Methods & Applications, 23:1 (1994), 15  crossref
    12. A. Yu. Veretennikov, “On large deviations for diffusion processes with measurable coefficients”, Russian Math. Surveys, 50:5 (1995), 977–987  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    13. A.Yu. Veretennikov, “On polynomial mixing bounds for stochastic differential equations”, Stochastic Processes and their Applications, 70:1 (1997), 115  crossref
    14. M. N. Malyshkin, “Subexponential Estimates of the Rate of Convergence to the Invariant Measure for Stochastic Differential Equations”, Theory Probab Appl, 45:3 (2001), 466  mathnet  crossref  mathscinet  isi  elib
    15. G. Aivaliotis, A.Yu. Veretennikov, “On Bellman's equations for mean and variance control of a Markov diffusion”, Stochastics An Int. J. of Probability & Stochastic Processes, 82:1 (2010), 41  crossref  elib
    16. N. Abourashchi, A. Yu. Veretennikov, “On stochastic averaging and mixing”, Theory Stoch. Process., 16(32):1 (2010), 111–129  mathnet  mathscinet
    17. A. Yu. Veretennikov, “On Sobolev solutions of Poisson equations in ℝ d with a parameter”, J Math Sci, 2011  crossref
    18. Johannes Ruf, “HEDGING UNDER ARBITRAGE”, Mathematical Finance, 2012, no  crossref
    19. A. Yu. Veretennikov, S. A. Klokov, “On local mixing conditions for SDE approximations”, Theory Probab. Appl., 57:1 (2013), 110–131  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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