Hilbert空間上一類半線性隨機發展方程的穩定性

Stability of A Class of Semilinear Stochastic Evolution Equations on Hilbert Space

摘要: 討論Hilbert空間上半線性隨機發展方程dY(t)=AY(t)+f(Y(t))dt+G(Y(t))dw(t)的穩定性。為此引進了適度解的正則性和常返性等概念,利用Liapunov直接法得到了此類隨機發展方程的隨機漸近穩定性、隨機指教穩定性、p-穩定性和幾乎必然指數穩定性的充分性判據。這些結果不但推廣了有限維情形的工作,同時也發展了A.Ichikawa的工作。

Abstract: Discusses the stability of semilinar stochastic evolution equations on Hilbert Space dY(t)=AY(t) +f(Y(t))dt + G(Y(t))dw(t). At first, in order to Study Stochatic asymp-totically stability, some concepts for mild-solution,, and the sufficiently conditions for this stability are obtained. Secondly, some new concepts of stability are defined. The main results make the finite dimensions extention and Ichika' results development.