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Conditional log-Laplace functional for a class of branching processes in random environments
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Hao Wang 《数学学报(英文版)》2015,31(1):71-90
A conditional log-Laplace functional(CLLF) for a class of branching processes in random environments is derived. The basic idea is the decomposition of a dependent branching dynamic into a no-interacting branching and an interacting dynamic generated by the random environments.CLLF will play an important role in the investigation of branching processes and superprocesses with interaction. 相似文献
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胡迪鹤 《数学物理学报(B辑英文版)》2006,26(3):431-442
The investigation for branching processes has a long history by their strong physics background, but only a few authors have investigated the branching processes in random environments. First of all, the author introduces the concepts of the multitype canonical Markov branching chain in random environment (CMBCRE) and multitype Markov branching chain in random environment (MBCRE) and proved that CMBCRE must be MBCRE, and any MBCRE must be equivalent to another CMBCRE in distribution. The main results of this article are the construction of CMBCRE and some of its probability properties. 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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胡迪鹤 《数学物理学报(A辑)》2010,30(5):1210-1241
该文系统地介绍随机环境中的马尔可夫过程. 共4章, 第一章介绍依时的随机环境中的马尔可夫链(MCTRE), 包括MCTRE的存在性及等价描述; 状态分类; 遍历理论及不变测度; p-θ 链的中心极限定理和不变原理. 第二章介绍依时的随机环境中的马尔可夫过程(MPTRE), 包括MPTRE的基本概念; 随机环境中的q -过程存在唯一性; 时齐的q -过程;MPTRE的构造及等价性定理.第三章介绍依时的随机环境中的分枝链(MBCRE), 包括有限维的和无穷维的MBCRE的模型和基本概念; 它们的灭绝概念;两极分化; 增殖率等.第四章介绍依时依空的随机环境中的马尔可夫链(MCSTRE), 包括MCSTRE的基本概念、构造; 依时依空的随机环境中的随机徘徊(RWSTRE)的中心极限定理、不变原理. 相似文献
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Andrew D. Barbour 《Stochastic Processes and their Applications》1976,4(1):33-40
In a Markov branching process with random environments, limiting fluctuations of the population size arise from the changing environment, which causes random variation of the ‘deterministic’ population prediction, and from the stochastic wobble around this ‘deterministic’ mean, which is apparent in the ordinary Markov branching process. If the random environment is generated by a suitable stationary process, the first variation typically swamps the second kind. In this paper, environmental processes are considered which, in contrast, lead to sampling and environmental fluctuation of comparable magnitude. The method makes little use either of stationarity or of the branching property, and is amenable to some generalization away from the Markov branching process. 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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Acta Mathematicae Applicatae Sinica, English Series - The class of population-size-dependent branching processes in independent identically distributed random environments is investigated. Under... 相似文献
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Gerd Rosenkranz 《随机分析与应用》2013,31(3):363-377
Conditions are established under which a sequence of density dependent branching processes with random environments converges weakly to a diffusion process. The limiting diffusion process can be obtained as a solution of a stochastic differential equation 相似文献
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本文研究了控制函数独立同分布,并且第n代的繁殖情况取决于环境的随机环境中分枝过程.给出了该模型稳定的充分条件,当环境平稳遍历时,得到了过程几乎处处灭绝的充分条件. 相似文献
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This paper establishes a stochastic differential equation system with both positive and negative jumps and proves the existence and uniqueness of the strong solution and presents an equivalent condition for ergodicity of the solution. The strong solution is called two-type continuous-state branching processes with immigration in Lévy random environments. The model can be extended to any finite dimensional case. 相似文献
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Mathematical Notes - The asymptotic behavior of the survival probability for multi-type branching processes in a random environment is studied. In the case where all particles are of one type, the... 相似文献
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A random walk with a branching system in random environments 总被引:1,自引:0,他引:1
We consider a branching random walk in random environments, where the particles are reproduced as a branching process with a random environment (in time), and move independently as a random walk on Z with a random environment (in locations). We obtain the asymptotic properties on the position of the rightmost particle at time n, revealing a phase transition phenomenon of the system. 相似文献
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Wei Gang Wang 《数学学报(英文版)》2011,27(5):897-904
We consider non-extinct branching processes in general random environments. Under the condition of means and second moments
of each generation being bounded, we give the upper bounds and lower bounds for some form deviations of the process. 相似文献
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D.P. Harrington 《Stochastic Processes and their Applications》1978,6(3):317-322
We prove necessary and sufficient conditions for the transience of the non-zero states in a non-homogeneous, continuous time Markov branching process. The result is obtained by passing from results about the discrete time skeleton of the continuous time chain to the continuous time chain itself. An alternative proof of a result for continuous time Markov branching processes in random environments is then given, showing that earlier moment conditions were not necessary. 相似文献