Almost periodic solutions for stochastic differential equations with Lévy noise
Almost periodic solutions for stochastic differential equations with Lévy noise
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DOI：
10.1088/0951-7715/25/10/2803
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发表时间：
2012-08
期刊：
影响因子：
1.7
通讯作者：
Yan Wang;Zhenxin Liu
中科院分区：
文献类型：
--
作者：
Yan Wang;Zhenxin Liu
引入了泊松概周期的概念。建立了一类具有无限维lsamvy噪声的线性和半线性随机微分方程的均方概周期解的存在唯一性。讨论了唯一均方概周期解的全局渐近稳定性。为了说明本文所得到的理论结果，考虑了依赖于空间变量的高斯噪声和泊松跳摄动的随机热方程。
The concept of Poisson almost periodicity is introduced. The existence and uniqueness of square-mean almost periodic solutions to some linear and semilinear stochastic differential equations with infinite dimensional Lévy noise are established provided the coefficients satisfy some suitable conditions. The global asymptotic stability of the unique square-mean almost periodic solution is discussed. To illustrate the theoretical results obtained in this paper, the stochastic heat equation perturbed by both Gaussian noise and Poisson jump dependent on spatial variables is considered.