Acta mathematica scientia,Series B ›› 2021, Vol. 41 ›› Issue (5): 1445-1473.doi: 10.1007/s10473-021-0504-7

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CONTINUOUS TIME MIXED STATE BRANCHING PROCESSES AND STOCHASTIC EQUATIONS

Shukai CHEN, Zenghu LI   

  1. Laboratory of Mathematics and Complex Systems, School of Mathematical Sciences, Beijing Normal University, Beijing 100875, China
  • Received:2020-03-20 Revised:2020-11-27 Online:2021-10-25 Published:2021-10-21
  • Contact: Shukai CHEN E-mail:skchen@mail.bnu.edu.cn
  • Supported by:
    The authors were supported by the National Key R&D Program of China (2020YFA0712900) and the National Natural Science Foundation of China (11531001).

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.

Key words: mixed state branching process, weak convergence, stochastic equation system, Wasserstein-type distance, stationary distribution

CLC Number: 

  • 60J80
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