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Wasserstein-Type Distances of Two-Type Continuous-State Branching Processes in Lévy Random Environments

Author

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  • Shukai Chen

    (Fujian Normal University)

  • Rongjuan Fang

    (Fujian Normal University)

  • Xiangqi Zheng

    (East China University of Science and Technology)

Abstract

Under natural conditions, we prove exponential ergodicity in the $$ L_1$$ L 1 -Wasserstein distance of two-type continuous-state branching processes in Lévy random environments with immigration. Furthermore, we express precisely the parameters of the exponent. The coupling method and the conditioned branching property play an important role in the approach. Using the tool of superprocesses, ergodicity in total variation distance is also proved.

Suggested Citation

  • Shukai Chen & Rongjuan Fang & Xiangqi Zheng, 2023. "Wasserstein-Type Distances of Two-Type Continuous-State Branching Processes in Lévy Random Environments," Journal of Theoretical Probability, Springer, vol. 36(3), pages 1572-1590, September.
    • Handle: RePEc:spr:jotpro:v:36:y:2023:i:3:d:10.1007_s10959-022-01211-y
    DOI: 10.1007/s10959-022-01211-y
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    References listed on IDEAS

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    1. Luo, Dejun & Wang, Jian, 2019. "Refined basic couplings and Wasserstein-type distances for SDEs with Lévy noises," Stochastic Processes and their Applications, Elsevier, vol. 129(9), pages 3129-3173.
    2. Hui He & Zenghu Li & Wei Xu, 2018. "Continuous-State Branching Processes in Lévy Random Environments," Journal of Theoretical Probability, Springer, vol. 31(4), pages 1952-1974, December.
    3. Li, Zenghu & Ma, Chunhua, 2015. "Asymptotic properties of estimators in a stable Cox–Ingersoll–Ross model," Stochastic Processes and their Applications, Elsevier, vol. 125(8), pages 3196-3233.
    4. Jianhai Bao & Feng‐Yu Wang & Chenggui Yuan, 2020. "Ergodicity for neutral type SDEs with infinite length of memory," Mathematische Nachrichten, Wiley Blackwell, vol. 293(9), pages 1675-1690, September.
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