Limit Theorems for a Strongly Supercritical Branching Process with Immigration in Random Environment

References

[1] V. I. Afanasyev, About time of reaching a high level by a random walk in a random environment, Theory Probab. Appl. 57 (2013), no. 4, 547–567. 10.1137/S0040585X97986175Suche in Google Scholar

[2] V. I. Afanasyev, On the time of attaining a high level by a transient random walk in a random environment, Theory Probab. Appl. 61 (2017), no. 2, 178–207. 10.1137/S0040585X97T988101Suche in Google Scholar

[3] V. I. Afanasyev, On the non-recurrent random walk in a random environment, Discrete Math. Appl. 28 (2018), no. 3, 139–156. 10.1515/dma-2018-0014Suche in Google Scholar

[4] V. I. Afanasyev, A critical branching process with immigration in random environment, Stochastic Process. Appl. 139 (2021), 110–138. 10.1016/j.spa.2021.05.001Suche in Google Scholar

[5] K. B. Athreya and P. E. Ney, Branching Processes, Grundlehren Math. Wiss. 196, Springer, New York, 1972. 10.1007/978-3-642-65371-1Suche in Google Scholar

[6] V. Bansaye, Cell contamination and branching processes in a random environment with immigration, Adv. in Appl. Probab. 41 (2009), no. 4, 1059–1081. 10.1239/aap/1261669586Suche in Google Scholar

[7] C. Böinghoff, Limit theorems for strongly and intermediately supercritical branching processes in random environment with linear fractional offspring distributions, Stochastic Process. Appl. 124 (2014), no. 11, 3553–3577. 10.1016/j.spa.2014.05.009Suche in Google Scholar

[8] E. Dyakonova, D. Li, V. Vatutin and M. Zhang, Branching processes in a random environment with immigration stopped at zero, J. Appl. Probab. 57 (2020), no. 1, 237–249. 10.1017/jpr.2019.94Suche in Google Scholar

[9] H. Kesten, M. V. Kozlov and F. Spitzer, A limit law for random walk in a random environment, Compos. Math. 30 (1975), 145–168. Suche in Google Scholar

[10] C. Smadi and V. Vatutin, Critical branching processes in random environment with immigration: Survival of a single family, Extremes 24 (2021), no. 3, 433–460. 10.1007/s10687-021-00413-7Suche in Google Scholar

[11] Y. Wang and Q. Liu, Limit theorems for a supercritical branching process with immigration in a random environment, Sci. China Math. 60 (2017), no. 12, 2481–2502. 10.1007/s11425-016-9017-7Suche in Google Scholar