Qualitative analysis of systems of Itô stochastic differential equations (Q2722155)

The authors presents a continuation of their investigations started in [Random Oper. Stoch Equ. 5, 203-216 (1997)], where a historical survey of results in this direction is proposed. For the inhomogeneous systems of Itô stochastic differential equations the notion of local invariance of surfaces and the notion of local first integral are introduced. Results which generally enable to find invariant surfaces and functionally independent first integrals of Itô stochastic differential equations are obtained. The method of finding invariant sets of Itô stochastic differential equations with the help of Lyapunov functions has been proposed by \textit{R. Z. Khas'minskij} [``Stabilität von Differentialgleichungssystemen bei zufälligen Störungen ihrer Parameter'' (1969; Zbl 0214.15903)].