Asymptotic Mean Square Stability Analysis for a Stochastic Delay Differential Equation

Abstract

: For a stochastic delay differential equation, a stability condition is derived in the sense of mean square stability. The condition substantiates the fact that noise with an appropriate power can reduce the influence of time delay in the differential equations. It is also illustrated by a numerical example. To derive the stability condition, the so-called domain subdivision method and Ito's formula are adopted.

Convergence and Confidence Intervals of Sample Paths of a Stochastic Differential Equation

“…For an end-fixed inverted pendulum, it was shown that stability is enhanced by the existence of noise with appropriate power [3]. The authors showed that the influence of time delay can be reduced by noise for a scalar stochastic delay system [4,5].…”