| Hilbert空间上一类半线性随机发展方程的稳定性 |
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| 引用本文： | 张志刚,秦明达.Hilbert空间上一类半线性随机发展方程的稳定性[J].北京科技大学学报,1998,20(1):93-98. |
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| 作者姓名： | 张志刚 秦明达 |
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| 作者单位： | 北京科技大学应用科学学院 |
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| 摘 要： | 讨论Ｈｉｌｂｅｒｔ空间上半线性随机发展方程ｄＹ（ｔ）＝（ＡＹ（ｔ）＋ｆ（Ｙ（ｔ）ｄｔ＋Ｇ（Ｙ（ｔ）ｄｗ（ｔ）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，随机指数稳定性，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。
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| 关 键 词： | 半线性 随机发展方程 稳定性 希尔伯特空间 |
Stability of A Class of Semilinear Stochastic Evolution Equations on Hilbert Space |
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| Zhang Zhigang, Qinh Mingda.Stability of A Class of Semilinear Stochastic Evolution Equations on Hilbert Space[J].Journal of University of Science and Technology Beijing,1998,20(1):93-98. |
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| Authors: | Zhang Zhigang Qinh Mingda |
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| Abstract: | 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. |
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| Keywords: | semilinear stochastic evolution equation mild solution Lyapunov method |
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