Kas'kun Y. Asymptotical behavior of unstable solutions of the stochastic differential equations

The asymptotical behavior of solutions of Ito's equations in the case of the irregular dependence of coefficients on a parameter is investigated. The sufficient conditions of an ergodicity, instability of solutions of Ito's stochastic differential equations are obtained. In case of unstable solutions the sufficient conditions of convergence of functionals of an integral type from unstable solutions of the stochastic differential equations are obtained. The theorem of The asymptotical behavior of some functions from solutions of the stochastic differential equations in the case of the irregular dependence of coefficients on a parameter is proved. The results is theoretical and can be used for investigation of research of dynamic systems with an irregular character of perturbations