两参数广义碰撞分枝过程被引量：1

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摘要本文考虑一类新的分枝过程:两参数碰撞分枝过程.对于这类过程,建立了正则性和唯一性判别准则.给出了两个吸收态的吸收概率和吸收时间的精确表达式.同时,给出了爆炸概率、爆炸时间以及全局逗留时间的精确表达式,揭示了次爆炸情形和超爆炸情形的不同性质.

作者陈安岳李俊平

机构地区 Department of Mathematics 香港大学统计与精算系中南大学数学科学与计算技术学院

出处《中国科学（A辑）》 CSCD 北大核心 2009年第8期915-932,共18页 Science in China(Series A)

基金香港研究资助局(批准号:HKU7010/06P) 国家自然科学基金(批准号:10771216) 教育部留学回国基金(批准号:[2007]1108)资助项目

关键词 Markov分枝过程广义碰撞分枝过程唯一性吸收概率平均吸收时间平均爆炸时间

参考文献16

1Harris T E. The Theory of Branching Processes. Berlin: Springer-Verlag, 1963.
2Athreya K B, Ney P E. Branching Processes. Berlin: Springer-Verlag, 1972.
3Asmussen S, Hering H. Branching Processes. Boston: Birkhauser, 1983.
4Sevastyanov B A. On certain types of Markov processes (in Russian). Uspehi Mat Nauk, 4:194 (1949).
5Ezhov I I. Branching processes with group death. Theory Probab Appl, 25:202-203 (1980).
6Kalinkin A V. Extinction probability of a branching process with interaction of particles. Theow Probab Appl, 27:201-205 (1982).
7Kalinkin A V. On the extinction probability of a branching process with two kinds of interaction of particles. Theory Probab Appl, 46:347-352 (2003).
8Chen A Y, Pollett P K, Zhang H J, et al. The collision branching process. J Appl Prob, 41:1033-1048 (2004).
9Chen R R. An extended class of time-continuous branching processes. J Appl Prob, 34:14 23 (1997).
10Chen A Y. Uniqueness and extinction properties of generalized Markov branching processes. J Math Anal Appl, 274:482-494 (2002).

1Sevastyanov B A. On certain types of Markov processes (in Russian). Uspehi Mat Nauk, 1949, 4:194.
2Ezhov I I. Branching processes with group death. Theory Probab Appl, 1980, 25:202-203.
3Kalinkin A V. Extinction probability of a branching process with interaction of particles. Theory Probab Appl, 1982, 27:201-205.
4Kalinkin A V. On the extinction probability of a branching process with two kinds of interaction of particles. Theory Probab Appl, 2003, 46:347-352.
5Chen A Y, Pollett P K, Zhang H J, et al. The collision branching process. J Appl Probab, 2004, 41:1033-1048.
6Foster J H. A limit theorem for a branching process with state-dependent immigration. Ann Math Statist, 1971, 42: 1773-1776.
7Pakes A G. A branching process with a state-dependent immigration component. Adv in Appl Probab, 1971, 3: 301 -314.
8Yamazato M. Some results on continuous time branching processes with state-dependent immigration. J Math Soc Japan, 1975, 27:479-496.
9Chen A Y, Renshaw E. Markov branching processes with instantaneous immigration. Frobab Theory Related Fields, 1990, 87:209-240.
10Chen A Y, Renshaw E. Recurrence of Markov branching processes with immigration. Stochastic Process Appl, 1993, 45:231-242.

1张红霞,李树君.带再生的碰撞分枝过程的吸收概率[J].数学理论与应用,2007,27(4):57-60.
2宋明珠.一类随机环境中可逗留随机游动的吸收概率[J].重庆工商大学学报（自然科学版）,2008,25(2):119-122.
3唐加山.具有吸收边界的二维随机游动的平均吸收时间[J].南京邮电学院学报,2000,20(4):41-43.
4喻娜.具有一个吸收壁的随机游动的平均吸收时间[J].重庆工商大学学报（自然科学版）,2007,24(1):6-8.
5李俊平,陈安岳.带移民和瞬态拯救的Markov分枝过程的存在唯一性与遍历性[J].中国科学（A辑）,2008,38(2):168-186.
6Huijie JI,Jinghai SHAO.First passage probabilities of one-dimensional diffusion processes[J].Frontiers of Mathematics in China,2015,10(4):901-916. 被引量：2
7任敏,张光辉.右半直线上依分布收敛独立随机环境中随机游动的吸收概率[J].山东大学学报（理学版）,2013,48(1):93-99. 被引量：2
8张红霞,李树君.一类带移民的加权分枝过程的有关结论[J].黑龙江科技信息,2010(27):217-217. 被引量：3
9黄月芳,史定华,熊勇.一维连续时间Markov分枝过程的密度演化方程[J].应用数学,2004,17(2):210-215.
10王燕.Multiplex网络上的平均吸收时间[J].哈尔滨师范大学自然科学学报,2016,32(2):85-86.

中国科学（A辑）

2009年第8期

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