Ergodicity and transience of SDEs driven by -stable processes with Markovian switching. Issue 7 (19th May 2018)

• Record Type: Journal Article
• Authors: Zhang, Zhenzhong; Jin, Xinghu; Tong, Jinying
• Is Part Of: Applicable analysis. Volume 97:Issue 7(2018)
• Page Start: 1187
• Page End: 1208
• Publication Date: 2018-05-19
• Subjects: Ergodicity -- Foster-Lyapunov criteria -- symmetric α-stable process -- Markovian switching -- M-matrix; 60J60 -- 60J27 -- 93E15; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2017.1307966
• Languages: English
• ISSNs: 0003-6811

Abstract

ABSTRACT: In this paper, we focus on ergodicity and transience of SDEs driven by symmetric α -stable processes ( α ∈ ( 1, 2 ) ) with Markovian switching. Some sufficient conditions for ergodicity of several classes of stable processes with Markovian switching are given. Furthermore, an almost necessary and sufficient condition for ergodicity of Ornstein–Uhlenbeck type driven by symmetric α -stable processes with Markovian switching is presented. As applications, some examples are provided to illustrate our results.