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Mat. Sb. (N.S.), 1979, Volume 109(151), Number 1(5), Pages 146–164 (Mi msb2362)  

This article is cited in 15 scientific papers (total in 15 papers)

Some new results in the theory of controlled diffusion processes

N. V. Krylov


Abstract: The validity of the Bellman equation for the payoff function for a controlled random diffusion process is proved. The main difference between the results in this article and those known earlier on the same theme is that here no assumptions whatever are made on the nondegeneracy of the controlled process. A theorem on the uniqueness of the solution of the Bellman equation is proved as well. The Bellman equation is examined in a lattice of measures; the derivatives of functions on which it is studied are understood as measures.
Bibliography: 13 titles.

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English version:
Mathematics of the USSR-Sbornik, 1980, 37:1, 133–149

Bibliographic databases:

UDC: 519.2+517.9
MSC: Primary 49C10, 60J60; Secondary 35K65
Received: 11.05.1977 and 07.12.1978

Citation: N. V. Krylov, “Some new results in the theory of controlled diffusion processes”, Mat. Sb. (N.S.), 109(151):1(5) (1979), 146–164; Math. USSR-Sb., 37:1 (1980), 133–149

Citation in format AMSBIB
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\by N.~V.~Krylov
\paper Some new results in the theory of controlled diffusion processes
\jour Mat. Sb. (N.S.)
\yr 1979
\vol 109(151)
\issue 1(5)
\pages 146--164
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\mathscinet{http://www.ams.org/mathscinet-getitem?mr=538554}
\zmath{https://zbmath.org/?q=an:0436.93055|0404.93052}
\transl
\jour Math. USSR-Sb.
\yr 1980
\vol 37
\issue 1
\pages 133--149
\crossref{https://doi.org/10.1070/SM1980v037n01ABEH001946}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1980KN98200009}


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  • http://mi.mathnet.ru/eng/msb/v151/i1/p146

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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, “On controlled diffusion processes with unbounded coefficients”, Math. USSR-Izv., 19:1 (1982), 41–64  mathnet  crossref  mathscinet  zmath
    2. N. V. Krylov, “On control of a diffusion process up to the time of first exit from a region”, Math. USSR-Izv., 19:2 (1982), 297–313  mathnet  crossref  mathscinet  zmath
    3. N. V. Krylov, “Boundedly nonhomogeneous elliptic and parabolic equations”, Math. USSR-Izv., 20:3 (1983), 459–492  mathnet  crossref  mathscinet  zmath
    4. P. L. Lions, “On the Hamilton–Jacobi–Bellman equations”, Acta Appl Math, 1:1 (1983), 17  crossref  mathscinet  zmath  isi
    5. N. V. Krylov, “Boundedly nonhomogeneous elliptic and parabolic equations in a domain”, Math. USSR-Izv., 22:1 (1984), 67–97  mathnet  crossref  mathscinet  zmath
    6. B. L. Rozovskii, “Filtering, Smoothing and Prediction of Degenerate Diffusion Processes. Backward Equations”, Theory Probab. Appl, 28:4 (1984), 762  mathnet  crossref
    7. N. V. Krylov, “An Approach to Controlled Diffusion Processes”, Theory Probab Appl, 31:4 (1987), 604  mathnet  crossref  isi
    8. 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
    9. 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
    10. 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
    11. Fleming W., Vermes D., “Convex Duality Approach to the Optimal-Control of Diffusions”, SIAM J. Control Optim., 27:5 (1989), 1136–1155  crossref  mathscinet  zmath  isi
    12. Nosovskij G., “Nonlinear Potentials for Hamilton–Jacobi–Bellman Equations”, Acta Appl. Math., 30:2 (1993), 101–123  crossref  mathscinet  zmath  isi
    13. Nosovskij G., “Nonlinear Potentials for Hamilton–Jacobi–Bellman Equations .2.”, Acta Appl. Math., 46:1 (1997), 29–48  crossref  mathscinet  zmath  isi
    14. Zhou W., “A Probabilistic Approach to Interior Regularity of Fully Nonlinear Degenerate Elliptic Equations in Smooth Domains”, Appl. Math. Optim., 67:3 (2013), 419–452  crossref  mathscinet  isi
    15. 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)
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