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Stochastic and deterministic control: Differential inequalities

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Stochastic Optimization

Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 81))

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References

  1. N.N. Krasovski and A.I. Subbotin. Positional Differential Games. Nauka, Moscow, 1974 (in Russian).

    Google Scholar 

  2. N.N. Krasovski. Differential games. Approximation and formal models (in Russian). Matematicheskie Sbornik, 107(7)(1978).

    Google Scholar 

  3. W.H. Fleming. The convergence problem for differential games. Journal of Mathematical Analysis and Applications, 3(1961).

    Google Scholar 

  4. L.S. Pontryagin. Linear differential games. II. Soviet Mathematics Doklady, 8(1967)910–912.

    Google Scholar 

  5. B.N. Pshenichnyi. The structure of differential games. Soviet Mathematics Doklady, 10(1969)70–72.

    Google Scholar 

  6. R. Isaacs. Differential Games. J. Wiley, New York, 1965.

    Google Scholar 

  7. A.I. Subbotin. Generalization of the main equation of differential game theory. Journal of Optimization Theory and Applications, 43(1984).

    Google Scholar 

  8. A.I. Subbotin and N.N. Subbotina. Properties of the potential of a differential game (in Russian). Prikladnaya Mathematika i Mekhanika, 46(1982).

    Google Scholar 

  9. V.F. Demyanov. Minimax: Directional Differentiation. Leningrad University Press, Leningrad, 1974.

    Google Scholar 

  10. S.N. Kruzkov. Generalization solutions of nonlinear first-order equations with many independent variables. I (in Russian). Matematicheskie Sbornik, 70(3)(1966).

    Google Scholar 

  11. N.V. Krylov. Controlled Diffusion Processes. Springer-Verlag, New York, 1980.

    Google Scholar 

  12. M.M. Hrustalev. Necessary and sufficient conditions of optimality in the form of the Bellman equation. Soviet Mathematics Doklady, 19(1978).

    Google Scholar 

  13. M.G. Crandall and P.L. Lions. Viscosity solutions of Hamilton-Jacobi equations. Transactions of the American Mathematical Society, 277(1983).

    Google Scholar 

  14. E.N. Barron, L.C. Evans and R. Jensen. Viscosity solutions of Isaacs' equations and differential games with Lipschitz conditions. Journal of Differential Equations, 53(1984).

    Google Scholar 

  15. R.S. Liptzer and A.N. Shiryaev. Statistics of Random Processes. Nauka, Moscow, 1974 (in Russian).

    Google Scholar 

  16. I.I. Gikman and A.V. Skorohod. Stochastic Differential Equations. Springer-Verlag, Berlin, 1972.

    Google Scholar 

  17. P. Bellman. Dynamic Programming. Princeton University Press, Princeton, New Jersey, 1957.

    Google Scholar 

  18. N.N. Krasovski and V.E. Tret'jakov. A saddle point of a stochastic differential game (in Russian). Doklady Akademii Nauk SSSR, 254(1980).

    Google Scholar 

  19. V.E. Tret'jakov. A program synthesis in a stochastic differential game (in Russian). Doklady Akademii Nauk SSSR, 270(1983).

    Google Scholar 

  20. J. Warga. Optimal Control of Differential and Functional Equations. Academic Press, 1972.

    Google Scholar 

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Authors and Affiliations

  1. Institute of Mathematics and Mechanics, Sverdlosk, USSR

    N. N. Subbotina, A. I. Subbotin & V. E. Tret'jakov

Authors
  1. N. N. Subbotina
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  2. A. I. Subbotin
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  3. V. E. Tret'jakov
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Editor information

Vadim I. Arkin A. Shiraev R. Wets

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© 1986 International Institute for Applied Systems Analysis

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Subbotina, N.N., Subbotin, A.I., Tret'jakov, V.E. (1986). Stochastic and deterministic control: Differential inequalities. In: Arkin, V.I., Shiraev, A., Wets, R. (eds) Stochastic Optimization. Lecture Notes in Control and Information Sciences, vol 81. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0007149

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  • DOI: https://doi.org/10.1007/BFb0007149

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-16659-7

  • Online ISBN: 978-3-540-39841-7

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