Annales de l'institut Henri Poincare (B) Probability and Statistics, 2014, том 50, выпуск 2, страницы 602–627 DOI: https://doi.org/10.1214/12-AIHP526(Mi aipps1)
Эта публикация цитируется в 26 научных статьях (всего в 26 статьях)
Conditional limit theorems for intermediately subcritical branching processes in random environment
Аннотация:
For a branching process in random environment it is assumed that the offspring distribution of the individuals varies in
a random fashion, independently from one generation to the other. For the subcritical regime a kind of phase transition appears. In
this paper we study the intermediately subcritical case, which constitutes the borderline within this phase transition. We study the
asymptotic behavior of the survival probability. Next the size of the population and the shape of the random environment conditioned
on non-extinction is examined. Finally we show that conditioned on non-extinction periods of small and large population
sizes alternate. This kind of ‘bottleneck’ behavior appears under the annealed approach only in the intermediately subcritical case.
This paper is a part of the research project ‘Branching processes and random walks in random environment’ supported by the German Research Foundation (DFG) and the Russian Foundation of Basic Research (RFBF, Grant DFG-RFBR 08-01-91954).
Поступила в редакцию: 13.01.2012 Исправленный вариант: 18.09.2012 Принята в печать: 24.09.2012
Xiequan Fan, Qi-Man Shao, “Self-normalized Cramér type moderate deviations for martingales and applications”, Bernoulli, 31:1 (2025)
Natalia Cardona-Tobón, Juan Carlos Pardo, “Speed of extinction for continuous state branching processes in subcritical Lévy environments: the strongly and intermediate regimes”, ALEA, 21:1 (2024), 741
Chun Mao Huang, Rui Zhang, Zhi Qiang Gao, “Precise Asymptotics in Limit Theorems for a Supercritical Branching Process with Immigration in a Random Environment”, Acta. Math. Sin.-English Ser., 2024
Wang Yanqing, Wang Dianni, Liu Jinling, Liu Quansheng, “Limit theorems for a supercritical two-type decomposable branching process in a random environment”, Sci. Sin.-Math., 2024
Ion Grama, Quansheng Liu, Eric Miqueu, “Asymptotics of the distribution and harmonic moments for a supercritical branching process in a random environment”, Ann. Inst. H. Poincaré Probab. Statist., 59:4 (2023)
В. А. Ватутин, Ш. Смади, “Критические ветвящиеся процессы в случайной среде с иммиграцией: размер единственного выжившего семейства”, Труды МИАН, 316 (2022), 355–375; V. A. Vatutin, C. Smadi, “Critical Branching Processes in a Random Environment with Immigration: The Size of the Only Surviving Family”, Proc. Steklov Inst. Math., 316 (2022), 336–355
Е. Е. Дьяконова, “Промежуточно докритический ветвящийся процесс в случайной среде: начальный этап эволюции”, Труды МИАН, 316 (2022), 129–144; E. E. Dyakonova, “Intermediately Subcritical Branching Process in a Random Environment: The Initial Stage of the Evolution”, Proc. Steklov Inst. Math., 316 (2022), 121–136
В. А. Ватутин, Е. Е. Дьяконова, “Многотипные ветвящиеся процессы в случайной среде”, УМН, 76:6 (2021), 71–118; V. A. Vatutin, E. E. Dyakonova, “Multitype branching processes in random environment”, Russian Math. Surveys, 76:6 (2021), 1019–1063
V. I. Afanasyev, “A critical branching process with immigration in random environment”, Stoch. Proc. Appl., 139 (2021), 110–138
Zhi-Qiang Gao, “Exact convergence rate in the central limit theorem for a branching process in a random environment”, Statistics & Probability Letters, 178 (2021), 109194
Doudou Li, Vladimir Vatutin, Mei Zhang, “Subcritical branching processes in random environment with immigration stopped at zero”, J. Theor. Probability, 34:2 (2021), 874–896
Yanqing Wang, Quansheng Liu, “Asymptotic Properties of a Supercritical Branching Process with Immigration in a Random Environment”, Stochastics and Quality Control, 36:2 (2021), 145
В. А. Ватутин, Е. Е. Дьяконова, “Свойства многотипных докритических ветвящихся процессов в случайной среде”, Дискрет. матем., 32:3 (2020), 3–23; V. A. Vatutin, E. E. D'yakonova, “Properties of multitype subcritical branching processes in random environment”, Discrete Math. Appl., 31:5 (2021), 367–382
В. А. Ватутин, Е. Е. Дьяконова, “Вероятность невырождения для одного класса
многотипных докритических ветвящихся процессов в случайной среде”, Матем. заметки, 107:2 (2020), 163–177; V. A. Vatutin, E. E. D'yakonova, “The Survival Probability for a Class of Multitype Subcritical Branching Processes in Random Environment”, Math. Notes, 107:2 (2020), 189–200
Xiequan Fan, Haijuan Hu, Quansheng Liu, “Uniform Cramér moderate deviations and Berry-Esseen bounds for a supercritical branching process in a random environment”, Front. Math. China, 15:5 (2020), 891
В. А. Ватутин, Е. Е. Дьяконова, “Многотипные слабо докритические ветвящиеся процессы в случайной среде”, Дискрет. матем., 31:3 (2019), 26–46; V. A. Vatutin, E. E. D'yakonova, “Multitype weakly subcritical branching processes in random environment”, Discrete Math. Appl., 31:3 (2021), 207–222
Vladimir Vatutin, Elena Dyakonova, “Path to survival for the critical branching processes in a random environment”, J. Appl. Probab., 54:2 (2017), 588–602
Ion Grama, Quansheng Liu, Eric Miqueu, “Harmonic moments and large deviations for a supercritical branching process in a random environment”, Electron. J. Probab., 22:none (2017)
Ion Grama, Quansheng Liu, Eric Miqueu, “Berry–Esseen's bound and Cramér's large deviation expansion for a supercritical branching process in a random environment”, Stochastic Processes and their Applications, 127:4 (2017), 1255
Discrete Time Branching Processes in Random Environment, 2017, 275
Обратная связь: