| 一类非自治随机微分方程的均方渐近概周期解 |
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| 引用本文： | 姚慧丽,王健伟.一类非自治随机微分方程的均方渐近概周期解[J].数学杂志,2016,36(2):319-327. |
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| 作者姓名： | 姚慧丽 王健伟 |
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| 作者单位： | 哈尔滨理工大学应用科学学院数学系, 黑龙江 哈尔滨 150080,哈尔滨理工大学应用科学学院数学系, 黑龙江 哈尔滨 150080 |
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| 基金项目： | 黑龙江省教育厅科学技术研究项目(12511110) |
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| 摘 要： | 本文研究了一类在可分Hilbert空间中的非自治随机微分方程的均方渐近概周期解.利用"Acquistapace-Terreni"条件,开方族和Banach不动点原理讨论了该类随机微分方程的均方渐近概周期解的存在唯一性,推广了该类随机微分方程的均方概周期解的存在唯一性问题.
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| 关 键 词： | 均方渐近概周期解 非自治随机微分方程 Banach不动点原理 |
| 收稿时间： | 2014/6/10 0:00:00 |
| 修稿时间： | 2015/3/23 0:00:00 |
SQUARE-MEAN ASYMPTOTICALLY ALMOST PERIODIC SOLUTION ON A CLASS OF NONAUTONOMOUS STOCHASTIC DIFFERENTIAL EQUATIONS |
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| YAO Hui-li and WANG Jian-wei.SQUARE-MEAN ASYMPTOTICALLY ALMOST PERIODIC SOLUTION ON A CLASS OF NONAUTONOMOUS STOCHASTIC DIFFERENTIAL EQUATIONS[J].Journal of Mathematics,2016,36(2):319-327. |
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| Authors: | YAO Hui-li and WANG Jian-wei |
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| Institution: | Department of Mathematics, School of Application and Science, Harbin University of Science and Technology, Harbin 150080, China and Department of Mathematics, School of Application and Science, Harbin University of Science and Technology, Harbin 150080, China |
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| Abstract: | In this papre, the square-mean asymptotically almost periodic solution is studied on a class of nonautonomous stochastic differential equations in a separable Hilbert space. By using the "Acquistapace-Terreni" conditions, evolution families and Banach fixed point theorem, the existence and uniqueness of square-mean asymptotically almost periodic solution on this kind of nonautonomous stochastic differential equations are discussed. The problems on the existence and uniqueness of square-mean almost periodic solutions on this kind of equation are generalized. |
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| Keywords: | square-mean asymptotically almost periodic solution nonautonomous stochastic differential equations Banach fixed point theory |
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