Stochastic Self-Stabilization
نویسنده
چکیده
Given a nonlinear It^ o equation dx(t)=f(x(t);t)dt+ug(x(t);t)dw(t), suppose that the equation is almost surely exponentially stable provided the noise intensity u is large enough. We show that if u is replaced by u= R t 0 jr(s)x(s)j p ds, then the equation stabilizes itself in the sense that R 1 0 jr(t)x(t)j p dt<1 a.s. Moreover, if u is replaced by u=sup 0t jr(s)x(s)j, then the equation stabilizes itself in the sense that sup 0t<1 jr(t)x(t)j<1 a.s.
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