Multi-condition of stability for nonlinear stochastic non-autonomous delay differential equation

Modern Stochastics: Theory and Applications

Leonid Shaikhet¹ 

[1] Tel-Aviv University;

关键词: Nonlinear stochastic differential equation;    order of nonlinearity higher than one;    varying coefficients;    discrete and distributed delays;    exponential mean square stability;    stability in probability;    regions of stability;   

DOI  :  10.15559/18-VMSTA110

来源: DOAJ

【 摘 要 】

A nonlinear stochastic differential equation with the order of nonlinearity higher than one, with several discrete and distributed delays and time varying coefficients is considered. It is shown that the sufficient conditions for exponential mean square stability of the linear part of the considered nonlinear equation also are sufficient conditions for stability in probability of the initial nonlinear equation. Some new sufficient condition of stability in probability for the zero solution of the considered nonlinear non-autonomous stochastic differential equation is obtained which can be considered as a multi-condition of stability because it allows to get for one considered equation at once several different complementary of each other sufficient stability conditions. The obtained results are illustrated with numerical simulations and figures.

【 授权许可】

Unknown