Abstract
It is shown that an Ornstein-Uhlenbeck type process associated with a spectrally
positive Lévy process can be obtained as the fluctuation limits of both discrete state and continuous state branching processes with immigration.
Publisher
Cambridge University Press (CUP)
Subject
Statistics, Probability and Uncertainty,General Mathematics,Statistics and Probability
Cited by
9 articles.
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1. On central limit theorems for branching processes with dependent immigration;Bulletin of Taras Shevchenko National University of Kyiv. Series: Physics and Mathematics;2020
2. Berry-Esseen bound for nearly critical branching processes with immigration;Bulletin of Taras Shevchenko National University of Kyiv. Series: Physics and Mathematics;2019
3. Ornstein–Uhlenbeck operators and semigroups;Russian Mathematical Surveys;2018-04
4. A fluctuation type limit theorem for Jiřina processes with immigration;Acta Mathematica Sinica, English Series;2009-07-15
5. A Weak Limit Theorem for Generalized Jiřina Processes;Journal of Applied Probability;2009-06