Exponential Ergodicity for SDEs Driven by α-Stable Processes with Markovian Switching in Wasserstein Distances

In this paper, we consider the ergodicity for stochastic differential equations driven by symmetric α -stable processes with Markovian switching in Wasserstein distances. Some sufficient conditions for the exponential ergodicity are presented by using the theory of M-matrix, coupling method and Lyap...

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Bibliographic Details
Published in:Potential analysis 2018-11, Vol.49 (4), p.503-526
Main Authors: Tong, Jinying, Jin, Xinghu, Zhang, Zhenzhong
Format: Article
Language:English
Subjects:
Differential equations
Economic models
Ergodic processes
Functional Analysis
Geometry
Liapunov functions
Markov analysis
Markov processes
Mathematics
Mathematics and Statistics
Ornstein-Uhlenbeck process
Potential Theory
Probability Theory and Stochastic Processes
Switching
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Summary:In this paper, we consider the ergodicity for stochastic differential equations driven by symmetric α -stable processes with Markovian switching in Wasserstein distances. Some sufficient conditions for the exponential ergodicity are presented by using the theory of M-matrix, coupling method and Lyapunov function method. As applications, the Ornstein-Uhlenbeck type process and some other processes driven by symmetric α -stable processes with Markovian switching are presented to illustrate our results. In addition, under some conditions, an explicit expression of the invariant measure for Ornstein-Uhlenbeck process is given.
ISSN:0926-2601
1572-929X
DOI:10.1007/s11118-017-9665-3