Poisson Stable Solutions for Stochastic Differential Equations with Lévy Noise

• Published in: Acta mathematica Sinica. English series Vol. 38; no. 1; pp. 22 - 54
• Main Authors: Liu, Xin, Liu, Zhen Xin
• Format: Journal Article
• Language: English
• Published: Beijing Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society 01.01.2022; Springer Nature B.V
• Subjects: Differential equations; Mathematical analysis; Mathematics; Mathematics and Statistics; 34C27; 34C25; 60H10; quasi-periodic solution; 60G51; Lévy noise; asymptotic stability; Levitan almost periodic solution; periodic solution; Poisson stable solution; almost periodic solution; 37B20; almost automorphic solution; Stochastic differential equation; Birkhoff recurrent solution

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) solutio...