| Contents |
| Consider the stochastic dynamical non linear system with the Wiener process and the Poisson jumps:
\begin{equation}\label{Puas1-vec2}
\begin{array}{c}
d {\bf x}(t)= \Bigl( P(t;{\bf x}(t)) + Q(t;{\bf x}(t)) \cdot {\bf
s}(t;{\bf x}(t))\Bigr) dt + \\
+ B(t;{\bf x}(t)) d {\bf
w}(t)+ \displaystyle\int_{\Gamma }
\Xi(t;{\bf x}(t);\gamma )\nu(dt;d\gamma ),
\end{array}
\end{equation}
where ${\bf x}\in \bf{R}^{n}$, $n\geq 2$; ${\bf w} (t)$ is the $m-$dimensional Wiener process; $\nu(t;\Delta\gamma)$ is the homogeneous with respect to $t$ non centered Poisson measure.
For such systems we construct the program control ${\bf
s}(t;{\bf x}(t))$ with probability one (PCP1), which allows the system (\ref{Puas1-vec2}) to move on the given manifold
$
\left\{g(t;{\bf x}(t))=0 \right\}
$
for each $t\in [0;T]$, $T\leq \infty$.
The control program ${\bf s}(t;{\bf x}(t))$ is solution for the algebraic system of linear equations. Considered method is based on the theory of the first integrals for stochastic differential equations systems. |
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