ПОСТРОЕНИЕ АСИМПТОТИЧЕСКИХ РЕШЕНИЙ СИНГУЛЯРНО ВОЗМУЩЕННОГО СТОХАСТИЧЕСКОГО ДИФФЕРЕНЦИАЛЬНОГО УРАВНЕНИЯ БЕСКОНЕЧНОГО ПОРЯДКА
Abstract
В данной работе предлагается алгоритм построения асимптотических решений сингулярно возмущенного стохастических дифференциального уравнения бесконечного порядка.
References
2. Carroll C., Tokuoka K., Wu W. The Method of Moderation for Solving Dynamic Stochastic Optimization Problems. — Paper provided by Society for Economic Dynamics in its series 2012 Meeting Papers with number 1102.
3. Marti K. Stochastic optimization methods. — Springer, Berlin Heidelberg, 2005. — ISBN: 978-3-662-46214-0.
4. Kabanov Yu.M., Pergamenshchikov S.M. Optimal control of singularly perturbed linear stochastic systems // Stochastics and Stoch. Rep. — 1991. —Vol.36 — C.109 – 135.
5. Kabanov Yu.M., Pergamenshchikov S.M., Stoyanov J.M. Asymptotic expansions for singularly perturbed stochastic differential equations // Stochastics and Stoch. Rep. – New Trend in Probability and Statistics, Proc. of the Bakuriani Coll. in Honour Yu.V. Prokhorov. V. 1, eds. V.V. Sazonov, T.L. Shervashidze, Mokslas, Vilnius; VSP, Utrecht, 1991. — pp. 413 – 435.
6. Stein, Jerome L. Stochastic Optimal Control, International Finance, and Debt Crises. – Oxford University Press, 2006. — ISBN: 978-0-199-28057-5.
7. Korobeinik Ju. Differential equations of infinite order and infinite systems of differential equations. Izv. Akad. Nauk SSSR Ser. Mat. Vol. 34, 1970. — pp. 881 – 922.
8. Krasnoselsky M.A., Zabreyko P.P. Geometrical methods of nonlinear analysis. Springer-Verlag, Berlin, 1984.
9. Lomov S. A. The construction of asymptotic solutions of certain problems with parameters. Izv. Akad. Nauk SSSR Ser. Mat. Vol. 32, 1968. — pp. 884 – 913.
10. Persidsky K.P. Izv. AN KazSSR, Ser. Mat. Mach., Issue 2, 1948. — pp. 3 – 34.
11. Skorokhod A. On infinite systems of stochastic differential equations // Methods Funct. Anal. Topology. Vol. 5, No. 4, 1999. — pp. 54 – 61.
12. Tihonov A. N. Uber unendliche Systeme von Differentialgleichungen. Rec. Math. Vol. 41, Issue 4, 1934. — pp. 551 – 555.
13. Tihonov A. N. Systems of differential equations containing small parameters in the derivatives. Mat. Sbornik N. S. Vol. 31, Issue 73, 1952. — pp. 575 – 586.
14. Vasil’eva A. B. Asymptotic behaviour of solutions of certain problems for ordinary non-linear differential equations with a small parameter multiplying the highest derivatives. Uspehi Mat. Nauk. Vol. 18, Issie 111, no. 3 , 1963. — pp. 15 – 86.
15. Zhautykov O. A. On a countable system of differential equations with variable parameters. Mat. Sb. (N.S.). Vol. 49, Issue 91, 1959. — pp. 317 – 330.
16. Zhautykov O. A. Extension of the Hamilton-Jacobi theorems to an infinite canonical system of equations. Mat. Sb. (N.S.). Vol. 53, Issue 95, 1961. — pp. 313 – 328.

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