Asymptotically almost automorphic solutions to stochastic differential equations driven by a Levy process
Asymptotically almost automorphic solutions to stochastic differential equations driven by a Levy process
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Levy 过程驱动的随机微分方程的渐近几乎自守解
DOI：
10.1080/17442508.2016.1178748
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发表时间：
2016
期刊：
影响因子：
--
通讯作者：
Tang Chao
中科院分区：
文献类型：
--
作者：
Chang Yong-Kui;Tang Chao
本文引入了随机过程的泊松渐近几乎自同构的新概念。然后，证明了这类过程空间的一些基本性质，包括复合定理。随后，应用这一概念，研究了一类线性和半线性随机微分方程在一定条件下分布渐近概自同构解的存在唯一性。最后，给出了一个算例来说明主要结果。
In this paper, a new concept of Poisson asymptotically almost automorphy for stochastic processes is introduced. And then, some fundamental properties including composition theorems for the space of such processes are proved. Subsequently, this concept is applied to investigate the existence and uniqueness of asymptotically almost automorphic solutions in distribution to some linear and semilinear stochastic differential equations driven by a Lévy process under some suitable conditions. Finally, an example is given to illustrate the main results.