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Teor. Veroyatnost. i Primenen., 1966, Volume 11, Issue 4, Pages 612–631 (Mi tvp662)  

This article is cited in 12 scientific papers (total in 12 papers)

On Stefan's problem and optimal stopping rules for Markov processes

B. I. Grigelionis, A. N. Shiryaev

Moscow

Abstract: Let $X=\{x_i,\zeta,\mathscr M_i,\mathbf P_x\}$ be a homogeneous Markov process with the phase space $E\subseteq R^n$. Let us denote $\tilde s(x)=\sup\limits_{\tau\in\mathfrak M}\mathbf M_xg(x_\tau)$ where $\mathfrak M$ is the class of Markov stopping moments. The purpose of this article is to find those conditions under which the finding of the optimal stopping moment $\widetilde\tau$ and the “cost” $\widetilde s(x)$ is equivalent to the solution of generalized Stefan's problem (5).

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English version:
Theory of Probability and its Applications, 1966, 11:4, 541–558

Bibliographic databases:

Received: 25.04.1966

Citation: B. I. Grigelionis, A. N. Shiryaev, “On Stefan's problem and optimal stopping rules for Markov processes”, Teor. Veroyatnost. i Primenen., 11:4 (1966), 612–631; Theory Probab. Appl., 11:4 (1966), 541–558

Citation in format AMSBIB
\Bibitem{GriShi66}
\by B.~I.~Grigelionis, A.~N.~Shiryaev
\paper On Stefan's problem and optimal stopping rules for Markov processes
\jour Teor. Veroyatnost. i Primenen.
\yr 1966
\vol 11
\issue 4
\pages 612--631
\mathnet{http://mi.mathnet.ru/tvp662}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=216709}
\zmath{https://zbmath.org/?q=an:0178.53303}
\transl
\jour Theory Probab. Appl.
\yr 1966
\vol 11
\issue 4
\pages 541--558
\crossref{https://doi.org/10.1137/1111060}


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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, “Control of Markov processes and $W$-spaces”, Math. USSR-Izv., 5:1 (1971), 233–266  mathnet  crossref  mathscinet  zmath
    2. N. V. Krylov, “On uniqueness of the solution of Bellman's equation”, Math. USSR-Izv., 5:6 (1971), 1387–1398  mathnet  crossref  mathscinet  zmath
    3. E. B. Frid, “On the semiregularity of boundary points for nonlinear equations”, Math. USSR-Sb., 23:4 (1974), 483–507  mathnet  crossref  mathscinet  zmath
    4. G. Kallianpur, O. A. Oleinik, “On free boundary problems arising in probability theory (uniqueness theorems)”, Russian Math. Surveys, 51:6 (1996), 1203–1205  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    5. E. V. Yagnyatinskii, “A problem of optimal sequential investing”, Russian Math. Surveys, 52:4 (1997), 850–851  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    6. Del Moral P., Guionnet A., “Large deviations for interacting particle systems: Applications to non–linear filtering”, Stochastic Processes and Their Applications, 78:1 (1998), 69–95  crossref  mathscinet  zmath  isi
    7. Dayanik S., Karatzas L., “On the optimal stopping problem for one–dimensional diffusions”, Stochastic Processes and Their Applications, 107:2 (2003), 173–212  crossref  mathscinet  zmath  isi
    8. Lototsky S.V., “Wiener chaos and nonlinear filtering”, Applied Mathematics and Optimization, 54:3 (2006), 265–291  crossref  mathscinet  zmath  isi
    9. Dayanik S., “Optimal stopping of linear diffusions with random discounting”, Mathematics of Operations Research, 33:3 (2008), 645–661  crossref  mathscinet  zmath  isi
    10. Theory Probab. Appl., 54:1 (2010), 14–28  mathnet  crossref  crossref  mathscinet  isi
    11. A. A. Muravlev, A. N. Shiryaev, “Two-sided disorder problem for a Brownian motion in a Bayesian setting”, Proc. Steklov Inst. Math., 287:1 (2014), 202–224  mathnet  crossref  crossref  isi  elib  elib
    12. D. I. Lisovskii, “Bayesian sequential testing problem for a Brownian bridge”, Theory Probab. Appl., 63:4 (2019), 556–579  mathnet  crossref  crossref  mathscinet  isi  elib
  • Теория вероятностей и ее применения Theory of Probability and its Applications
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