Hilbert空间上一类半线性随机发展方程的稳定性

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

讨论Ｈｉｌｂｅｒｔ空间上半线性随机发展方程ｄＹ的稳定性。为此引进了适度解的正则性和常返性等概念，利用Ｌｉａｐｕｎｏｖ直接法得到了此类随机发展方程的随机渐近稳定性、随机指教稳定性、ｐ－稳定性和几乎必然指数稳定性的充分性判据。这些结果不但推广了有限维情形的工作，同时也发展了Ａ．Ｉｃｈｉｋａｗａ的工作。

Discusses the stability of semilinar stochastic evolution equations on Hilbert Space dY(t) = [AY(t) +f(Y(t))]dt + G(Y(t))d (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.