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

Nguyen Quy Hy; Nguyen Thi Minh

Annales Polonici Mathematici (1992)

- Volume: 57, Issue: 1, page 1-12
- ISSN: 0066-2216

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topNguyen Quy Hy, and Nguyen Thi Minh. "A simulation of integral and derivative of the solution of a stochastici integral equation." Annales Polonici Mathematici 57.1 (1992): 1-12. <http://eudml.org/doc/262278>.

@article{NguyenQuyHy1992,

abstract = {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 $x^\{\prime \}_u(t)$.},

author = {Nguyen Quy Hy, Nguyen Thi Minh},

journal = {Annales Polonici Mathematici},

keywords = {stochastic integral equation; Markov chain; integral representation of a solution},

language = {eng},

number = {1},

pages = {1-12},

title = {A simulation of integral and derivative of the solution of a stochastici integral equation},

url = {http://eudml.org/doc/262278},

volume = {57},

year = {1992},

}

TY - JOUR

AU - Nguyen Quy Hy

AU - Nguyen Thi Minh

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

JO - Annales Polonici Mathematici

PY - 1992

VL - 57

IS - 1

SP - 1

EP - 12

AB - 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 $x^{\prime }_u(t)$.

LA - eng

KW - stochastic integral equation; Markov chain; integral representation of a solution

UR - http://eudml.org/doc/262278

ER -

## References

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- [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). Zbl0127.06102
- [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).

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