A sufficient condition of existence of a time-dependent solution to the Fokker-Planck equation (Q1975783)

The deterministic system governed by the ordinary differential equation \(\dot{x} = f(x)\), \(x \in \mathbb{R}^n\), \(f(x) \in \mathbb{R}^n\), is considered. The author analyzes its behavior in the presence of white noise. A sufficient condition of existence of a time-independent solution is obtained for the Fokker-Planck equation used in the analysis of stochastic ordinary differential equations. It is shown that the theorem proved in this study can serve as a basis for constructing an algorithm of approximate computation of the time-independent solution.