Ergodicity and transience of SDEs driven by alpha-stable processes with Markovian switching

摘要

In this paper, we focus on ergodicity and transience of SDEs driven by symmetric alpha-stable processes (alpha is an element of (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 alpha-stable processes with Markovian switching is presented. As applications, some examples are provided to illustrate our results.