Exponential stability of linear stochastic differential equations with bounded delay and the W-transform

Electronic Journal of Qualitative Theory of Differential Equations

R. I. Kadiev¹  Arkadi Ponosov² 

[1] Dagestan Scientific Center, Russian Academy of Sciences, Makhachkala, Russia;Norwegian University of Life Sciences, As, Norway;

DOI  :  10.14232/ejqtde.2008.1.23

来源: DOAJ

【 摘 要 】

We demonstrate how the method of auxiliary ('reference') equations, also known as N. V. Azbelev's W-transform method, can be used to derive efficient conditions for the exponential Lyapunov stability of linear delay equations driven by a vector-valued Wiener process. For the sake of convenience the W-method is briefly outlined in the paper, its justification is however omitted. The paper contains a general stability result, which is specified in the last section in the form of seven corollaries providing sufficient stability conditions for some important classes of It\^{o} equations with delay.

【 授权许可】

Unknown