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Izv. Akad. Nauk SSSR Ser. Mat., 1981, Volume 45, Issue 4, Pages 734–759 (Mi izv1583)  

This article is cited in 10 scientific papers (total in 10 papers)

On controlled diffusion processes with unbounded coefficients

N. V. Krylov


Abstract: The paper is devoted to the general theory of controlled diffusion processes in a domain of a $d$-dimensional space in the absence of constraints on the growth of the coefficients at infinity. It turned out that the most suitable object of study is the payoff function in the optimal stopping problem for the controlled process. A theory analogous to the theory of controlled processes in the whole space, with growth constraints on the coefficients, is developed under natural assumptions.
Bibliography: 16 titles.

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English version:
Mathematics of the USSR-Izvestiya, 1982, 19:1, 41–64

Bibliographic databases:

UDC: 517.9
MSC: 60J60, 65G40, 93E20
Received: 29.10.1980

Citation: N. V. Krylov, “On controlled diffusion processes with unbounded coefficients”, Izv. Akad. Nauk SSSR Ser. Mat., 45:4 (1981), 734–759; Math. USSR-Izv., 19:1 (1982), 41–64

Citation in format AMSBIB
\Bibitem{Kry81}
\by N.~V.~Krylov
\paper On~controlled diffusion processes with unbounded coefficients
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1981
\vol 45
\issue 4
\pages 734--759
\mathnet{http://mi.mathnet.ru/izv1583}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=631436}
\zmath{https://zbmath.org/?q=an:0514.93070|0497.93060}
\transl
\jour Math. USSR-Izv.
\yr 1982
\vol 19
\issue 1
\pages 41--64
\crossref{https://doi.org/10.1070/IM1982v019n01ABEH001410}


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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 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
    2. N. V. Krylov, “Boundedly nonhomogeneous elliptic and parabolic equations”, Math. USSR-Izv., 20:3 (1983), 459–492  mathnet  crossref  mathscinet  zmath
    3. N. V. Krylov, “On degenerate nonlinear elliptic equations. II”, Math. USSR-Sb., 49:1 (1984), 207–228  mathnet  crossref  mathscinet  zmath
    4. N. V. Krylov, “Boundedly nonhomogeneous elliptic and parabolic equations in a domain”, Math. USSR-Izv., 22:1 (1984), 67–97  mathnet  crossref  mathscinet  zmath
    5. N. V. Krylov, “On unconditional solvability of the Bellman equation with constant coefficients in convex domains”, Math. USSR-Sb., 63:2 (1989), 289–303  mathnet  crossref  mathscinet  zmath
    6. 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
    7. 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
    8. Joseph B. Keller, Hans F. Weinberger, “Boundary and initial boundary-value problems for separable backward–forward parabolic problems”, J Math Phys (N Y ), 38:8 (1997), 4343  crossref  mathscinet  zmath
    9. O. Alvarez, “A quasilinear elliptic equation in ℝN”, Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 126:05 (2011), 911  crossref
    10. D. B. Rokhlin, “On the dynamic programming principle for controlled diffusion processes in a cylindrical region”, Sib. elektron. matem. izv., 10 (2013), 302–310  mathnet
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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