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Izv. Akad. Nauk SSSR Ser. Mat., 1972, Volume 36, Issue 1, Pages 248–261 (Mi izv2297)  

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

On control of the solution of a stochastic integral equation with degeneration

N. V. Krylov


Abstract: This paper is devoted to the derivation of Bellman's differential equation in the payoff function $v(x)$ for a broad class of cases (Theorems 1 and 2). We prove that $v(x)$ is the smallest solution of this equation (Theorem 3).

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English version:
Mathematics of the USSR-Izvestiya, 1972, 6:1, 249–262

Bibliographic databases:

UDC: 519.2
MSC: Primary 60H20, 49C15; Secondary 49A30
Received: 24.12.1970

Citation: N. V. Krylov, “On control of the solution of a stochastic integral equation with degeneration”, Izv. Akad. Nauk SSSR Ser. Mat., 36:1 (1972), 248–261; Math. USSR-Izv., 6:1 (1972), 249–262

Citation in format AMSBIB
\Bibitem{Kry72}
\by N.~V.~Krylov
\paper On~control of the solution of a stochastic integral equation with degeneration
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1972
\vol 36
\issue 1
\pages 248--261
\mathnet{http://mi.mathnet.ru/izv2297}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=307342}
\zmath{https://zbmath.org/?q=an:0265.60056}
\transl
\jour Math. USSR-Izv.
\yr 1972
\vol 6
\issue 1
\pages 249--262
\crossref{https://doi.org/10.1070/IM1972v006n01ABEH001874}


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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 uniqueness of the solution of Bellman's equation”, Math. USSR-Izv., 5:6 (1971), 1387–1398  mathnet  crossref  mathscinet  zmath
    2. N. V. Krylov, “On control of the solution of a stochastic integral equation with degeneration”, Math. USSR-Izv., 6:1 (1972), 249–262  mathnet  crossref  mathscinet  zmath
    3. 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
    4. M. V. Safonov, “On the Dirichlet problem for Bellman's equation in a plane domain”, Math. USSR-Sb., 31:2 (1977), 231–248  mathnet  crossref  mathscinet  zmath  isi
    5. P. L. Lions, “Formule de trotter et equations de Hamilton–Jacobi–Bellman”, Calcolo, 17:4 (1980), 321  crossref  mathscinet
    6. J. L. Menaldi, “On the Optimal Stopping Time Problem for Degenerate Diffusions”, SIAM J Control Optim, 18:6 (1980), 697  crossref  mathscinet  zmath  isi
    7. Avner Friedman, Pierre-Louis Lions, “The Optimal Strategy in the Control Problem Associated with the Hamilton–Jacobi–Bellman Equation”, SIAM J Control Optim, 18:2 (1980), 191  crossref  mathscinet  zmath  isi
    8. P. L. Lions, “Sum probleils related to the relliian-dzrzchlet equation for two opepators”, Communications in Partial Differential Equations, 5:7 (1980), 753  crossref
    9. P. L. Lions, “Control of diffusion processes inRN”, Comm Pure Appl Math, 34:1 (1981), 121  crossref  mathscinet  zmath
    10. N. V. Krylov, “Boundedly nonhomogeneous elliptic and parabolic equations”, Math. USSR-Izv., 20:3 (1983), 459–492  mathnet  crossref  mathscinet  zmath
    11. Pierre-Louis Lions, “Sur les equations de Monge-Ampere. I”, manuscripta math, 41:1-3 (1983), 1  crossref  mathscinet  zmath  isi
    12. P. L. Lions, “On the Hamilton–Jacobi–Bellman equations”, Acta Appl Math, 1:1 (1983), 17  crossref  mathscinet  zmath  isi
    13. N. V. Krylov, “On degenerate nonlinear elliptic equations. II”, Math. USSR-Sb., 49:1 (1984), 207–228  mathnet  crossref  mathscinet  zmath
    14. P. L Linos, “Optimal control of diffustion processes and Hamilton–Jacobi–Bellman equations part I: the dynamic programming principle and application”, Communications in Partial Differential Equations, 8:10 (1983), 1101  crossref
    15. Pierre-Louis Lions, “Sur les equations de Monge-Ampère”, Arch Rational Mech Anal, 89:2 (1985), 93  crossref  mathscinet  zmath  adsnasa
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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