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《Advances in Applied Mathematics》1988,9(1):56-86
A measure-valued process which carries genealogical information is defined for a supercritical branching random field with immigration. This process counts the particles present at a final time whose ancestors had specified locations at given times in the past. A law of large numbers and a fluctuation limit theorem are proved for this process under a space-time scaling. The fluctuation limit is a nonstationary generalized Ornstein-Uhlenbeck process. An example of interest in transport theory and polymer chemistry is given. 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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For a supercritical branching process (Zn) in a stationary and ergodic environment ξ, we study the rate of convergence of the normalized population Wn=Zn/E[Zn|ξ] to its limit W∞: we show a central limit theorem for W∞−Wn with suitable normalization and derive a Berry-Esseen bound for the rate of convergence in the central limit theorem when the environment is independent and identically distributed. Similar results are also shown for Wn+k−Wn for each fixed k∈N∗. 相似文献
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In the present paper, we characterize the behavior of supercritical branching processes in random environment with linear fractional offspring distributions, conditioned on having small, but positive values at some large generation. As it has been noticed in previous works, there is a phase transition in the behavior of the process. Here, we examine the strongly and intermediately supercritical regimes The main result is a conditional limit theorem for the rescaled associated random walk in the intermediately case. 相似文献
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O. A. Butkovsky 《Mathematical Notes》2012,92(5-6):612-618
A generalization of the Sevast’yanov branching process with immigrationwhich is a Cox process is studied. The generating function of the number of particles of the process is obtained. For critical processes, the limit behavior of the number of particles at infinity is established. 相似文献
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Hua Ming Wang 《数学学报(英文版)》2013,29(6):1095-1110
In this paper, we study the total number of progeny, W, before regenerating of multitype branching process with immigration in random environment. We show that the tail probability of |W| is of order t-κ as t→∞, with κ some constant. As an application, we prove a stable law for (L-1) random walk in random environment, generalizing the stable law for the nearest random walk in random environment (see "Kesten, Kozlov, Spitzer: A limit law for random walk in a random environment. Compositio Math., 30, 145-168 (1975)"). 相似文献
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LI YingQiu HU YangLi & LIU QuanSheng College of Mathematics Computing Sciences Changsha University of Science Technology Changsha China College of Mathematics Computer Sciences Hunan Normal University Changsha LMAM University of Bretgne-Sud BP Vannes France 《中国科学 数学(英文版)》2011,(7)
Let W be the limit of the normalized population size of a supercritical branching process in a varying or random environment. By an elementary method, we find sufficient conditions under which W has finite weighted moments of the form EWpl(W), where p > 1, l 0 is a concave or slowly varying function. 相似文献
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Probability Theory and Related Fields - 相似文献
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Norman Kaplan 《Stochastic Processes and their Applications》1974,2(3):281-294
A limit theorem is proven for the integral of a general class of population processes possessing independent immigration components. For the special case of the Bellman-Harris process with immigration, further results are obtained. 相似文献
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We consider a branching random walk with a random environment in time, in which the offspring distribution of a particle of generation n and the distribution of the displacements of its children depend on an environment indexed by the time n. The environment is supposed to be independent and identically distributed. For A ?, let Zn(A) be the number of particles of generation n located in A. We show central limit theorems for the counting measure Zn(·) with appropriate normalization. 相似文献
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I. Rahimov 《Statistics & probability letters》2011,81(8):907-914
In this paper, we consider the conditional least squares estimator (CLSE) of the offspring mean of a branching process with non-stationary immigration based on the observation of population sizes. In the supercritical case, assuming that the immigration variables follow known distributions, conditions guaranteeing the strong consistency of the proposed estimator will be derived. The asymptotic normality of the estimator will also be proved. The proofs are based on direct probabilistic arguments, unlike the previous papers, where functional limit theorems for the process were used. 相似文献
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Let Z(t) be the population at time t of a critical age-dependent branching process. Suppose that the offspring distribution has a generating function of the form f(s) = s + (1 ? s)1+αL(1 ? s) where α ∈ (0, 1) and L(x) varies slowly as x → 0+. Then we find, as t → ∞, (P{Z(t)> 0})αL(P{Z(t)>0})~ μ/αt where μ is the mean lifetime of each particle. Furthermore, if we condition the process on non-extinction at time t, the random variable P{Z(t)>0}Z(t) converges in law to a random variable with Laplace-Stieltjes transform 1 - u(1 + uα)?1/α for u ?/ 0. Moment conditions on the lifetime distribution required for the above results are discussed. 相似文献
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A.G. Pakes 《Stochastic Processes and their Applications》1976,4(2):175-185
Some limit theorems are obtained for the population size of a critical Bienaymé-Galton-Watson process allowing immigration and where the variance of the offspring distribution is infinite. An application is given to a limit theorem for the situation where the immigration does not occur but the population size is conditioned on non-extinction until the remote future. This complements a well-known result of Slack. 相似文献