Resumen de Barbashin-Krasovskii theorem for stochastic differential equations

Oleksiy Ignatyev, V. Mandrekar

• A system of stochastic differential equations which has a zero solution is considered. It is assumed that there exists a positive definite function such that the corresponding operator is nonpositive. It is proved that if the set does not include entire semitrajectories of the system almost surely, then the zero solution is asymptotically stable in probability.