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Continuous Time Mixed State Branching Processes and Stochastic Equations

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Abstract

A continuous time and mixed state branching process is constructed by a scaling limit theorem of two-type Galton-Watson processes. The process can also be obtained by the pathwise unique solution to a stochastic equation system. From the stochastic equation system we derive the distribution of local jumps and give the exponential ergodicity in Wasserstein-type distances of the transition semigroup. Meanwhile, we study immigration structures associated with the process and prove the existence of the stationary distribution of the process with immigration.

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Authors and Affiliations

  1. Laboratory of Mathematics and Complex Systems, School of Mathematical Sciences, Beijing Normal University, Beijing, 100875, China

    Shukai Chen  (陈舒凯) & Zenghu Li  (李增沪)

Authors
  1. Shukai Chen  (陈舒凯)
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  2. Zenghu Li  (李增沪)
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Corresponding author

Correspondence to Shukai Chen  (陈舒凯).

Additional information

The authors were supported by the National Key R&D Program of China (2020YFA0712900) and the National Natural Science Foundation of China (11531001).

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Chen, S., Li, Z. Continuous Time Mixed State Branching Processes and Stochastic Equations. Acta Math Sci 41, 1445–1473 (2021). https://doi.org/10.1007/s10473-021-0504-7

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  • DOI: https://doi.org/10.1007/s10473-021-0504-7

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