Open Access
Issue
Wuhan Univ. J. Nat. Sci.
Volume 31, Number 3, June 2026
Page(s) 291 - 298
DOI https://doi.org/10.1051/wujns/2026313291
Published online 24 June 2026
  1. Smith W L. Necessary conditions for almost sure extinction of a branching process with random environment[J]. The Annals of Mathematical Statistics, 1968, 39(7): 2136-2140. [Google Scholar]
  2. Smith W L, Wilkinson W E. On branching processes in random environments[J]. The Annals of Mathematical Statistics, 1969, 40(3): 814-827. [Google Scholar]
  3. Smith W L, Wilkinson W E. Branching processes in Markovian environments[J]. Duke Mathematical Journal, 1971, 38(4): 749-763. [Google Scholar]
  4. Athreya K B, Karlin S. On branching processes with random environments I: Extinction probabilities[J]. The Annals of Mathematical Statistics, 1971, 42(5): 1499-1520. [Google Scholar]
  5. Athreya K B, Karlin S. On branching processes with random environments II: Extinction probabilities[J]. The Annals of Mathematical Statistics, 1971, 42(6): 184-185. [Google Scholar]
  6. Holzheimer J. φ-Branching processes in a random environment[J]. Applicationes Mathematicae, 1983, 18(3): 351-358. [Google Scholar]
  7. Yanev G P, Yanev N M. Extinction of controlled branching processes in random environments[J]. Mathematica Balkanica, New Series, 1990, 4(6): 368-380. [Google Scholar]
  8. Bi Q X, Li J F. Controlled branching processes in random environments[J]. Journal of Mathematics, 2003, 23(4): 437-442(Ch). [Google Scholar]
  9. Li Y Q, Li D R, Pan S, et al. Limit theorems for controlled branching processes in random environments[J]. Acta Mathematica Sinica, Chinese Series, 2018, 61(2): 317-326(Ch). [Google Scholar]
  10. Key E S. Limiting distributions and regeneration times for multitype branching processes with immigration in a random environment[J]. The Annals of Probability, 1987, 15(1): 344-353. [Google Scholar]
  11. Li Y Q, Liu Q S. Branching processes with migration in random environments[J]. Journal of Xiangtan University (Natural Science Edition), 2009, 31(3): 18-22(Ch). [Google Scholar]
  12. Ren M, Wang J J. Limiting behaviors of the bisexual branching processes with migration in random environments[J]. Journal of Jilin Institute of Chemical Technology, 2020, 37(11): 85-90(Ch). [Google Scholar]
  13. Li D D, Zhang M. Asymptotic behaviors for critical branching processes with immigration[J]. Acta Mathematica Sinica, English Series, 2019, 35(4): 537-549. [Google Scholar]
  14. Wang Y Q, Liu Q S. Limit theorems for a supercritical branching process with immigration in a random environment[J]. Science China Mathematics, 2017, 60(12): 2481-2502(Ch). [Google Scholar]
  15. Ren M. Limit properties for branching process affected by communicable diseases in random environments[J]. Journal of Zhejiang University (Science Edition), 2022, 49(1): 53-59(Ch). [Google Scholar]
  16. Ren M, Wang J J, Wang Y P. Probability generating functions and extinction conditions for the bisexual branching process affected by infectivity of virus in random environments[J]. Journal of Wuhan University (Natural Science Edition), 2021, 67(3): 263-269(Ch). [Google Scholar]
  17. Sun W, Liu W, Li D R. Limit properties for branching process with immigration in random environment[J]. Mathematical Theory and Applications, 2013, 33(4): 1-5(Ch). [Google Scholar]
  18. Wang Y Q, Liu Q S. Berry-Esseen's bound for a supercritical branching process with immigration in a random environment[J]. Scientia Sinica Mathematica, 2021, 51(5): 751-762(Ch). [Google Scholar]
  19. Zubkov A M. Analogies between Galton-Watson processes and branching processes[J]. Theory of Probability & Its Applications, 1975, 19(2): 309-331. [Google Scholar]
  20. Ren M, Zhang G H. Some properties of branching processes with random control functions and affected by viral infectivity in random environments[J]. Advances in Continuous and Discrete Models, 2023, 2023(1): 1-18. [Google Scholar]
  21. Song M Z, Wu Y F. Complete convergence for moving average processes under m-WOD random variables[J]. Wuhan University Journal of Natural Sciences, 2024, 29(6): 529-538. [Google Scholar]

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