论文标题
带有Lévy噪声的随机微分方程的泊松稳定解决方案
Poisson stable solutions for stochastic differential equations with Lévy noise
论文作者
论文摘要
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无限的尺寸lévy噪音，大跳。在漂移，扩散和跳跃系数的适当条件下，我们证明存在继承系数的泊松稳定性的解决方案。此外，我们表明这些解决方案在全球渐近稳定。最后，我们通过几个示例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 Lévy 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.
