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A stochastic integral equation corresponding to a probability space $(\Omega ,{\Sigma }_{\omega },P_{\omega })$ is considered. This equation plays the role of a dynamical system in many problems of stochastic control with the control variable $u\left(·\right):{ℝ}^1\to {ℝ}^m$. One constructs stochastic processes ${\eta }^{\left(1\right)}\left(t\right)$, ${\eta }^{\left(2\right)}\left(t\right)$ connected with a Markov chain and with the space $(\Omega ,{\Sigma }_{\omega },P_{\omega })$. The expected values of ${\eta }^{\left(i\right)}\left(t\right)$ (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 $x_u^{\text{'}}\left(t\right)$.