AM  Vol.2 No.7 , July 2011
Analysis of Noise under Regime Switching
Author(s) Ling Bai, Xiaoyue Li
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.

Cite this paper
nullL. Bai and X. Li, "Analysis of Noise under Regime Switching," Applied Mathematics, Vol. 2 No. 7, 2011, pp. 836-842. doi: 10.4236/am.2011.27112.
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