数学物理学报(英文版) ›› 2021, Vol. 41 ›› Issue (5): 1445-1473.doi: 10.1007/s10473-021-0504-7

• 论文 • 上一篇    下一篇

CONTINUOUS TIME MIXED STATE BRANCHING PROCESSES AND STOCHASTIC EQUATIONS

陈舒凯, 李增沪   

  1. Laboratory of Mathematics and Complex Systems, School of Mathematical Sciences, Beijing Normal University, Beijing 100875, China
  • 收稿日期:2020-03-20 修回日期:2020-11-27 出版日期:2021-10-25 发布日期:2021-10-21
  • 通讯作者: Shukai CHEN E-mail:skchen@mail.bnu.edu.cn
  • 作者简介:Zenghu LI,E-mail:lizh@bnu.edu.cn
  • 基金资助:
    The authors were supported by the National Key R&D Program of China (2020YFA0712900) and the National Natural Science Foundation of China (11531001).

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).

摘要: 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.

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

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

中图分类号: 

  • 60J80