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数学进展 - 2018, Vol. 47(2): 259-276
研究论文
Lèvy 过程驱动的随机泛函积分—微分方程的概周期解
On Almost Periodic Solutions forStochastic Functional Integro-differential Evolution Equations with Lèvy Noise

徐丽平1,2,罗交晚1,李治2
XU Liping1,2, LUO Jiaowan1, LI Zhi2,*

1.广州大学数学与信息学院, 广州, 广东, 510006;
2. 长江大学信息与数学学院, 荆州, 湖北, 434023
1. School of Mathematics and Information Sciences,Guangzhou University, Guangzhou, Guangdong, 510006, P. R. China;
2. School of Information and Mathematics,Yangtze University, Jingzhou, Hebei, 434023, P. R. China

收稿日期: 2016-05-27
出版日期: 2018-05-16
2018, Vol. 47(2): 259-276
DOI: 10.11845/sxjz.2016070b


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摘要 本文研究一类Levy过程驱动的无穷维随机泛函积分---微分发展方程.在一些合适的条件下, 使用算子半群理论和不动点方法,这些方程的概周期温和解的存在唯一性被讨论.进一步,为了说明我们的结果,一个例子被提出.
关键词 概周期性随机泛函积分—微分发展方程vy噪声    
Abstract:In this paper, we investigate a class of stochastic functional integro-differential evolution equations with infinite dimensional Lèvy noise. Under some suitable assumptions, the existence and uniqueness of almost periodic mild solutions in distribution to these equations are discussed by means of semigroups of operators and fixed point method. Moreover, an example is given to illustrate our results.
Key wordsAlmost periodicity in distribution    Stochastic functional integro-differential evolution equations       vy noise
PACS:  O211.63  
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[1] 董一林. Lévy过程驱动的带局部Lipschitz系数的随机微分方程解的遍历性[J]. 数学进展, 2018, 47(1): 11-30.
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