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2018 A user-friendly condition for exponential ergodicity in randomly switched environments
Michel Benaïm, Tobias Hurth, Edouard Strickler
Electron. Commun. Probab. 23: 1-12 (2018). DOI: 10.1214/18-ECP148


We consider random switching between finitely many vector fields leaving positively invariant a compact set. Recently, Li, Liu and Cui showed in [12] that if one the vector fields has a globally asymptotically stable (G.A.S.) equilibrium from which one can reach a point satisfying a weak Hörmander-bracket condition, then the process converges in total variation to a unique invariant probability measure. In this note, adapting the proof in [12] and using results of [5], the assumption of a G.A.S. equilibrium is weakened to the existence of an accessible point at which a barycentric combination of the vector fields vanishes. Some examples are given which demonstrate the usefulness of this condition.


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Michel Benaïm. Tobias Hurth. Edouard Strickler. "A user-friendly condition for exponential ergodicity in randomly switched environments." Electron. Commun. Probab. 23 1 - 12, 2018.


Received: 13 March 2018; Accepted: 28 June 2018; Published: 2018
First available in Project Euclid: 25 July 2018

zbMATH: 1397.60106
MathSciNet: MR3841405
Digital Object Identifier: 10.1214/18-ECP148

Primary: 34A37, 37A50, 60J25, 93C30, 93E15


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