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Continuous-State Branching Processes with Immigration

  • Zenghu LiEmail author
Chapter
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Part of the Mathematical Lectures from Peking University book series (MLPKU)

Abstract

This work provides a brief introduction to continuous-state branching processes with or without immigration. The processes are constructed by taking rescaling limits of classical discrete-state branching models. We give quick developments of the martingale problems and stochastic equations of the continuous-state processes. The proofs here are more elementary than those appearing in the literature before. We have made them readable without requiring too much preliminary knowledge on branching processes and stochastic analysis. Using the stochastic equations, we give characterizations of the local and global maximal jumps of the processes. Under suitable conditions, their strong Feller property and exponential ergodicity are studied by a coupling method based on one of the stochastic equations.

Keywords

Continuous-state branching process Immigration Rescaling limit Martingale problem Stochastic equation Strong Feller property Exponential ergodicity 

Mathematics Subject Classification (2010)

60J80 60J85 60H10 60H20 

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© Springer Nature Singapore Pte Ltd. 2020

Authors and Affiliations

  1. 1.School of Mathematical SciencesBeijing Normal UniversityBeijingChina

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