Analysis of Noise under Regime Switching

Ling Bai, Xiaoyue Li

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DOI: 10.4236/am.2011.27112                

Abstract

In this paper we consider a stochastic nonlinear system under regime switching. Given a system x(t)=f(x(t),r(t),t) in which f satisfies so-called one-side polynomial growth condition. We introduce two Brownian noise feedbacks and stochastically perturb this system into dx(t)=(x(t),r(t),t)dt+ σ (r(t))|x(t)|^βx(t)dW₁(t)+q(r(t))x(t)dW₂(t) . It can be proved that appropriate noise intensity may suppress the potentially explode in a finite time and ensure that this system is almost surely exponentially stable although the corresponding system without Brownian noise perturbation may be unstable system.

Keywords

Hybrid System, One-Side Polynomial Growth Condition, Ito Formula, Stochastic Ultimate Boundedness

Conflicts of Interest

The authors declare no conflicts of interest.

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