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# Wydawnictwa / Czasopisma IMPAN / Annales Polonici Mathematici / Wszystkie zeszyty

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

### Tom 57 / 1992

Annales Polonici Mathematici 57 (1992), 1-12 DOI: 10.4064/ap-57-1-1-12

#### Streszczenie

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 $x'_u(t)$.

• Hy Nguyen
• Minh Nguyen

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