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Continuous-State Branching Processes with Immigration

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From Probability to Finance

Part of the book series: Mathematical Lectures from Peking University ((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.

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Authors and Affiliations

  1. School of Mathematical Sciences, Beijing Normal University, Beijing, 100875, China

    Zenghu Li

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  1. Zenghu Li
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Correspondence to Zenghu Li .

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Editors and Affiliations

  1. Institut de Science Financière et d’Assurances, Université Claude Bernard Lyon 1, Lyon, France

    Ying Jiao

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Li, Z. (2020). Continuous-State Branching Processes with Immigration. In: Jiao, Y. (eds) From Probability to Finance. Mathematical Lectures from Peking University. Springer, Singapore. https://doi.org/10.1007/978-981-15-1576-7_1

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