Abstract
In this paper, we explore the relationship between exponential convergence to a unique quasi-stationary distribution, the existence of an exponentially ergodic Q-process for a symmetric Markov process and ultracontractivity of its associated semigroup. In particular, it is shown that intrinsic ultracontractivity implies uniform convergence to the Q-process under suitable assumptions. Another goal is to specify some parameters related to the underlying quasi-stationary distribution and Q-process.
Funding Statement
Supported by Postgraduate Scientific Research Innovation Project of Hunan Province (CX20210613).
Acknowledgments
The authors are grateful to the referee for the careful reading of the first version of the paper and for helpful comments and suggestions.
Citation
Hanjun Zhang. Huasheng Li. Saixia Liao. "Intrinsic ultracontractivity and uniform convergence to the Q-process for symmetric Markov processes." Electron. Commun. Probab. 28 1 - 12, 2023. https://doi.org/10.1214/23-ECP550
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