Exponential ergodicity for SDEs driven by \(\alpha\)-stable processes with Markovian switching in Wasserstein distances
type: Item
instance of: scholarly article
title: Exponential ergodicity for SDEs driven by \(\alpha\)-stable processes with Markovian switching in Wasserstein distances
zbMATH Open document ID: 1426.60083
author: Jinying Tong
author: Xinghu Jin
author: Zhen Zhong Zhang
published in: Potential Analysis
publication date: 2018-10-04T00:00:00Z
review text: The object of study is an SDE with Markovian switching regime of the form \[dX_t=a(X_t,Y_t)dt+\sigma(X_t,Y_t)dZ_t,\] where \((Z_t)\) is a symmetric \(\alpha\)-stable Lévy process with \(\alpha\in(0,2)\) and \((Y_t)\) is a right-continuous Markov chain with finite state-space, independent of \((Z_t)\). The usual assumtions for existence and uniqueness of \((X_t)\) are supposed, i.e.,\ for fixed state the coefficient \(a\) is global Lipschitz continuous, \(\sigma\) is \(\gamma\)-Hölder continuous for \(\gamma\in\{\frac1{\alpha},1\}\) and the coefficients \(a,\sigma\) together fulfill a linear growth condition. The authors give sufficient conditions for exponential ergodicity in the Wasserstein distance of the Markovian semigroup \((P_t)\) of \((X_t,Y_t)\) to its stationary distribution using the theory of M-matrices, the coupling method and Lyapunov functionals.
Mathematics Subject Classification ID: 60H10
Mathematics Subject Classification ID: 60G52
Mathematics Subject Classification ID: 60J27
Mathematics Subject Classification ID: 60J75
Mathematics Subject Classification ID: 93E15
zbMATH DE Number: 6947312
zbMATH Keywords: exponential ergodicity
zbMATH Keywords: symmetric \(\alpha\)-stable process
zbMATH Keywords: Markovian switching
zbMATH Keywords: M-matrix
zbMATH Keywords: Wasserstein distance
zbMATH Keywords: coupling method
MaRDI profile type: Publication
full work available at URL: s11118-017-9665-3
OpenAlex ID: W2770030679
Wikidata QID: Q115602908
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DOI: 10.1007/S11118-017-9665-3
description: scientific article; zbMATH DE number 6947312