Skip to main content
Log in

Moments of Continuous-State Branching Processes in Lévy Random Environments

  • Published:
Acta Mathematica Scientia Aims and scope Submit manuscript

Abstract

For continuous-state branching processes in Lévy random environments, the recursion of n-moments and the equivalent condition for the existence of general f-moments are established, where f is a positive continuous function satisfying some standard conditions.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Luschgy H, Pagès G. Moment estimates for Lévy processes. Electron Commun Prob, 2008, 13: 422–434

    Article  MATH  Google Scholar 

  2. Li Z. Measure-Valued Branching Markov Processes. Heidelberg: Springer-Verlag, 2011

    Book  MATH  Google Scholar 

  3. Gün O, König W, Sekulovió O. Moment asymptotics for branching random walks in random environment. Electron J Probab, 2013, 18(63): 1–18

    MathSciNet  Google Scholar 

  4. Agarwal R, Hristova S, Kopanov P, O’regan D. Impulsive differential equations with Gamma distributed moments of impulses and p-moment exponential stability. Acta Mathematica Scientia, 2017, 37B(4): 985–997

    Article  MathSciNet  MATH  Google Scholar 

  5. Qiu D, Chen P, Andrei V. Complete moment convergence for LP-mixingales. Acta Mathematica Scientia, 2017, 37B(5): 1319–1330

    Article  MATH  Google Scholar 

  6. Zhao Y. Asymptotic properties of the moment convergence for NA sequences. Acta Mathematica Scientia, 2014, 34B(2): 301–312

    Article  MathSciNet  MATH  Google Scholar 

  7. Barczy M, Li Z, Pap G. Moment formulas for multitype continuous state and continuous time branching process with immigration. J Theor Probab, 2016, 29(3): 958–995

    Article  MathSciNet  MATH  Google Scholar 

  8. Ji L, Li Z. Moments of continuous-state branching processes with or without immigration. 2017[2018-03-31]. https://arxiv.org/abs/1702.08698

  9. Jirina M. Stochastic branching processes with continuous state space. Czech Math J, 1958, 8: 292–313

    MathSciNet  MATH  Google Scholar 

  10. Bansaye V, Millan J C P, Smadi C. On the extinction of continuous state branching processes with catastrophes. Electron J Probab, 2013, 18(106): 1–31

    MathSciNet  MATH  Google Scholar 

  11. Palau S, Pardo J C. Continuous state branching processes in random environment: the Brownian case. Stoch Process Appl, 2017, 127: 957–994

    Article  MathSciNet  MATH  Google Scholar 

  12. He H, Li Z, Xu W. Continuous-state branching processes in Lévy random environments. J Theor Probab, 2017[2018-03-31]. https://doi.org/10.1007/s10959-017-0765-1

  13. Palau S, Pardo J C. Branching processes in a Lévy random environment. Acta Appl Math, 2018, 153(1): 55–79

    Article  MathSciNet  MATH  Google Scholar 

  14. Dawson D A, Li Z. Stochastic equations, flows and measure-valued processes. Ann Probab, 2012, 40(2): 813–857

    Article  MathSciNet  MATH  Google Scholar 

  15. Caballero M E, Lambert A, Uribe Bravo G. Proof(s) of the Lamperti representation of continuous-state branching processes. Probab Surv, 2009, 6: 62–89

    Article  MathSciNet  MATH  Google Scholar 

  16. Sato K I. Lévy Processes and Infinitely Divisible Distributions. Cambridge University Press, 1999

    MATH  Google Scholar 

  17. Athreya K B, Ney P E. Branching Processes. Berlin: Springer, 1972

    Book  MATH  Google Scholar 

Download references

Acknowledgements

Heartfelt thanks are given to Professor Zenghu Li for his careful guidance and helpful suggestions.

Author information

Authors and Affiliations

Authors

Corresponding authors

Correspondence to Lina Ji or Xiangqi Zheng.

Additional information

The authors are supported by the National Natural Science Foundation of China (11531001).

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Ji, L., Zheng, X. Moments of Continuous-State Branching Processes in Lévy Random Environments. Acta Math Sci 39, 781–796 (2019). https://doi.org/10.1007/s10473-019-0310-7

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10473-019-0310-7

Key words

2010 MR Subject Classification

Navigation