共查询到18条相似文献,搜索用时 62 毫秒
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测度值分枝过程与移民过程 总被引:8,自引:0,他引:8
本文介绍了测度值分枝过程和由斜卷积半群定义的伴随移民过程的基本理论和研究现状,主要内容包括:分枝粒子系统的收敛;超过程的基本正则性和极限定理;非线性微分方程;广义分枝模型;斜卷积半群和进入律;用Kuznetsov过程构造移民过程等。 相似文献
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本文主要考虑带移民的n维分枝过程的分枝性质和衰减性质.对于这类过程,首先给出了分枝性质的等价条件,得到了衰减指数的精确值λ_Z,同时进一步讨论λ_Z-不变向量/测度和拟平稳分布. 相似文献
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考虑独立同分布的随机环境中带移民的上临界分枝过程(Zn).应用(Zn)与随机环境中不带移民分枝过程的联系,以及与相应随机游动的联系,在一些适当的矩条件下,本文证明关于log Zn的中心极限定理的Berry-Esseen界. 相似文献
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本文考虑一类带移民和拯救的碰撞分枝过程(BCPIR)的存在唯—性、常返性以及临界爆炸情形下的衰减性质.首先深入讨论了BCIR q-矩阵发生函数的性质,建立了过程的唯一性判别准则,得到了一些比较好的过程常返性充分条件;并且通过发生函数给出了临界爆炸情形下关于连通类Z+的衰减指数λz的精确值.同时,进一步讨论λz-不变测度/不变向量,给出了λz-不变测度的发生函数. 相似文献
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本文在独立同分布的随机环境下,建立带有移民的两性分枝过程{Zn}n≥0,且移民人口数依赖当前人口数,证得{Zn}n≥0和{(Fn,Mn)}n≥1是随机环境中的马氏链,并得到第n代每个配对单元平均增长率{rk}k≥0的极限性质,从而推广了经典两性分枝过程的相关理论. 相似文献
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考虑了一类带有拯救的碰撞分枝过程,给出了过程的正则性与唯一性准则,并得到了常返性和遍历性的充要条件.同时,给出了指数遍历性的一个便于验证的充分条件. 相似文献
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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. 相似文献
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通过求解由轨道空间上的Poisson随机测度驱动的随机积分方程,对于满足Yamada-Watanabe型条件的移民速度函数,本文给出了带相依移民连续状态分枝过程的构造.此构造改进了Dawson和Li (2003)、Fu和Li (2004)和Li (2011)等在Lipschitz条件下的结果. 相似文献
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Yu Qiang Li 《数学学报(英文版)》2011,27(7):1333-1344
A relationship between continuous state population-size-dependent branching (CSDB) processes with or without immigration and
discrete state population-size-dependent branching (DSDB) processes with or without immigration is established via the representation
of the former. Based on this relationship, some limiting distributions of CSDB processes with or without immigration are obtained. 相似文献
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LI WenBo V 《中国科学 数学(英文版)》2012,55(11):2259-2271
We consider the small value probability of supercritical continuous state branching processes with immigration.From Pinsky(1972) it is known that under regularity condition on the branching mechanism and immigration mechanism,the normalized population size converges to a non-degenerate finite and positive limit W as t tends to infinity.We provide sharp estimate on asymptotic behavior of P(W≤ε) as ε→ 0+ by studying the Laplace transform of W.Without immigration,we also give a simpler proof for the small value probability in the non-subordinator case via the prolific backbone decomposition. 相似文献
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A space-time clustering model for historical earthquakes 总被引:3,自引:0,他引:3
This paper describes a generalization of Hawkes' self-exciting process in which each event creates a process of offspring with conditional intensity governed by a diffusion kernel. The process may be described as a space-time branching process with immigration, the immigration representing a background series of independent events. The model can be fitted by likelihood methods. As an illustration it is fitted to the catalogue of historical Italian earthquakes. 相似文献
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Pei-Sen Li 《数学学报(英文版)》2017,33(8):1021-1038
The nonlinear branching process with immigration is constructed as the pathwise unique solution of a stochastic integral equation driven by Poisson random measures. Some criteria for the regularity, recurrence, ergodicity and strong ergodicity of the process are then established. 相似文献
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《随机分析与应用》2013,31(3):721-738
Abstract Seneta (Seneta, E. The stationary distribution of a branching process allowing immigration: A remark on the critical case. J. Royal Statistical Society, Series B 1968, 30, 176–179) shows that a critical branching process with pure immigration has a stationary-limiting distribution provided that its offspring variance is infinite. We obtain a stationary-limiting distribution keeping the variance finite but allowing an emigration–immigration component in each generation. 相似文献