Poisson Stable Solutions for Stochastic Differential Equations with Levy Noise
Poisson Stable Solutions for Stochastic Differential Equations with Levy Noise
复制标题
带 Levy 噪声的随机微分方程的泊松稳定解
DOI：
10.1007/s10114-021-0107-1
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发表时间：
2022
期刊：
影响因子：
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通讯作者：
Liu Zhenxin
中科院分区：
文献类型：
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作者：
Liu Xin;Liu Zhenxin
本文在统一的框架下研究了无穷维Levy噪声驱动的半线性随机微分方程的Poisson稳定解（包括平稳解、周期解、拟周期解、概周期解、概自守解、Birkhoff常返解、Bebutov意义下的概常返解、Levitan概周期解、伪周期解、伪常返解和Poisson稳定解）.在适当的漂移、扩散和跳跃系数条件下，我们证明了存在解继承系数的Poisson稳定性。进一步证明了这些解在平方平均意义下是全局渐近稳定的。最后，我们通过几个例子来说明我们的理论结果。
In this paper, we use a unified framework to study Poisson stable (including stationary, periodic, quasi-periodic, almost periodic, almost automorphic, Birkhoff recurrent, almost recurrent in the sense of Bebutov, Levitan almost periodic, pseudo-periodic, pseudo-recurrent and Poisson stable) solutions for semilinear stochastic differential equations driven by infinite dimensional Levy noise with large jumps. Under suitable conditions on drift, diffusion and jump coefficients, we prove that there exist solutions which inherit the Poisson stability of coefficients. Further we show that these solutions are globally asymptotically stable in square-mean sense. Finally, we illustrate our theoretical results by several examples.