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1992 | 57 | 1 | 1-12
Tytuł artykułu

A simulation of integral and derivative of the solution of a stochastici integral equation

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
A stochastic integral equation corresponding to a probability space $(Ω,Σ_ω,P_ω)$ is considered. This equation plays the role of a dynamical system in many problems of stochastic control with the control variable $u(·):ℝ^1 → ℝ^m$. One constructs stochastic processes $η^{(1)}(t)$, $η^{(2)}(t)$ connected with a Markov chain and with the space $(Ω,Σ_ω,P_ω)$. The expected values of $η^{(i)}(t)$ (i = 1,2) are respectively the expected value of an integral representation of a solution x(t) of the equation and that of its derivative $x'_u(t)$.
Słowa kluczowe
Rocznik
Tom
57
Numer
1
Strony
1-12
Opis fizyczny
Daty
wydano
1992
otrzymano
1988-08-30
poprawiono
1989-07-20
Twórcy
  • Faculty of Mathematics, Mechanics and Informatics, Hanoi University, Hanoi, Vietnam
  • Faculty of Mathematics, Mechanics and Informatics, Hanoi University, Hanoi, Vietnam
Bibliografia
  • [1] Nguyen Ngoc Cuong, On a solution of a class of random integral equations relating to the renewal theory by the Monte-Carlo method, Ph. D. Thesis, University of Hanoi, 1983.
  • [2] N. Dunford and J. Schwartz, Linear Operators I, Interscience Publ., New York 1958.
  • [3] S. M. Ermakov and V. S. Nefedov, On the estimates of the sum of the Neumann series by the Monte-Carlo method, Dokl. Akad. Nauk SSSR 202 (1) (1972), 27-29 (in Russian).
  • [4] S. M. Ermakov, Monte Carlo Method and Related Problems, Nauka, Moscow 1975 (in Russian).
  • [5] Yu. M. Ermolev, Methods of Stochastic Programming, Nauka, Moscow 1976 (in Russian).
  • [6] Yu. M. Ermolev, Finite Difference Method in Optimal Control Problems, Naukova Dumka, Kiev 1978 (in Russian).
  • [7] W. H. Fleming and R. W. Rishel, Deterministic and Stochastic Optimal Control, Springer, Berlin 1975.
  • [8] I. I. Gikhman and A. V. Skorokhod, Introduction to the Theory of Random Processes, Saunders, Philadelphia 1965.
  • [9] Nguyen Quy Hy, On a probabilistic model for derivation and integration of the solution of some stochastic linear equations, Proc. Conf. Appl. Prob. Stat. Vietnam 1 (10-11), Nhatrang 7-1983.
  • [10] Nguyen Quy Hy and Nguyen Ngoc Cuong, On probabilistic properties of a solution of a class of random integral equations, Acta Univ. Lodz. Folia Math. 2 (1985).
  • [11] Nguyen Quy Hy and Nguyen Van Huu, A probabilistic model to solve a problem of stochastic control, Proc. Conf. Math. Vietnam III, Hanoi 7-1985.
  • [12] Nguyen Quy Hy and Bui Huy Quynh, Solution of a random integral using Monte-Carlo method, Bull. Univ. Hanoi Vol. Math. Mech. 10 (1980).
  • [13] L. V. Kantorovich and G. P. Akilov, Functional Analysis in Normed Spaces, Gos. Izdat. Fiz.-Mat. Liter., Moscow 1959 (in Russian).
  • [14] A. I. Khisamutdinov, A unit class of estimates for calculating functionals of solutions to II kind integral equations by the Monte Carlo method, Zh. Vychisl. Mat. i Mat. Fiz. 10 (5) (1970), 1269-1280 (in Russian).
  • [15] Bui Huy Quynh, On a randomised model for solving stochastic integral equation of the renewal theory, Bull. Univ. Hanoi Vol. Math. Mech. 11 (1980).
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-apmv57z1p1bwm
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