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

Nguyen Quy Hy; Nguyen Thi Minh

Annales Polonici Mathematici, Tome 57 (1992), p. 1-12 / Harvested from The Polish Digital Mathematics Library

Résumé

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 $u (\cdot) : ℝ^{1} \to ℝ^{m}$ . 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 $x_{u}^{'} (t)$ .

Publié le : 1992-01-01

Zbl 0755.60043

EUDML-ID : urn:eudml:doc:262278

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Nguyen Quy Hy; Nguyen Thi Minh. A simulation of integral and derivative of the solution of a stochastici integral equation. Annales Polonici Mathematici, Tome 57 (1992) pp. 1-12. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-apmv57z1p1bwm/

Bibliographie

[000] [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.

[001] [2] N. Dunford and J. Schwartz, Linear Operators I, Interscience Publ., New York 1958. | Zbl 0084.10402

[002] [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). | Zbl 0251.65002

[003] [4] S. M. Ermakov, Monte Carlo Method and Related Problems, Nauka, Moscow 1975 (in Russian).

[004] [5] Yu. M. Ermolev, Methods of Stochastic Programming, Nauka, Moscow 1976 (in Russian).

[005] [6] Yu. M. Ermolev, Finite Difference Method in Optimal Control Problems, Naukova Dumka, Kiev 1978 (in Russian).

[006] [7] W. H. Fleming and R. W. Rishel, Deterministic and Stochastic Optimal Control, Springer, Berlin 1975.

[007] [8] I. I. Gikhman and A. V. Skorokhod, Introduction to the Theory of Random Processes, Saunders, Philadelphia 1965. | Zbl 0132.37902

[008] [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.

[009] [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).

[010] [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.

[011] [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).

[012] [13] L. V. Kantorovich and G. P. Akilov, Functional Analysis in Normed Spaces, Gos. Izdat. Fiz.-Mat. Liter., Moscow 1959 (in Russian). | Zbl 0127.06102

[013] [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).

[014] [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).