Stability of the zero solution of nonlinear differential equations under the influence of white noise

Advances in Difference Equations

Irada Dzhalladova²  Miroslava Rikov³  Viera toudkov Rikov⁴ 

[1] Brno University of Technology, Brno, Czech Republic;Kiev National Economics Vadym Hetman University, Kyiv, Ukraine;University of Žilina, Žilina, Slovakia

关键词: stochastic systems;    white noise;    mean square stability;    Lyapunov function;    34K50;    60H10;    60H30;    65C30;   

DOI  :  10.1186/s13662-015-0482-y

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

The paper deals with a system of nonlinear differential equations under the influence of white noise. This system can be used as a mathematical model of various real problems in finance, mathematical biology, climatology, signal theory and others. Necessary and sufficient conditions for the asymptotic mean square stability of the zero solution of this system are derived in the paper. The paper introduces a new approach to studying such problems - construction of a suitable deterministic system with the use of Lyapunov function.

【 授权许可】

CC BY