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A unifying approach to non-minimal quasi-stationary distributions for one-dimensional diffusions

Part of: Markov processes Probability theory on algebraic and topological structures

Published online by Cambridge University Press:  08 August 2022

Kosuke Yamato Open the ORCID record for Kosuke Yamato [Opens in a new window]
Kosuke Yamato*
Affiliation:
Kyoto University
*
*Postal address: Department of Mathematics, Graduate School of Science, Kyoto University, Kyoto, Japan. Email address: yamato.kosuke.43r@st.kyoto-u.ac.jp
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Abstract

We study convergence to non-minimal quasi-stationary distributions for one-dimensional diffusions. We give a method for reducing the convergence to the tail behavior of the lifetime via a property we call the first hitting uniqueness. We apply the results to Kummer diffusions with negative drift and give a class of initial distributions converging to each non-minimal quasi-stationary distribution.

Keywords

One-dimensional diffusion processesquasi-stationary distributionslimit theoremsKummer diffusion processes

MSC classification

Primary: 60J60: Diffusion processes
Secondary: 60B10: Convergence of probability measures
Type
Original Article
Information
Journal of Applied Probability , Volume 59 , Issue 4 , December 2022 , pp. 1106 - 1128
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Copyright
© The Author(s), 2022. Published by Cambridge University Press on behalf of Applied Probability Trust

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