Relevant bibliographies by topics / Extinction population branching processes

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Academic literature on the topic 'Extinction population branching processes'

Author: Grafiati
Published: 24 April 2022

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Journal articles on the topic "Extinction population branching processes"

1

Wang, Han-xing. "Extinction of population-size-dependent branching processes in random environments." Journal of Applied Probability 36, no. 1 (1999): 146–54. http://dx.doi.org/10.1239/jap/1032374237.

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We generalize a population-size-dependent branching process to a more general branching model called the population-size-dependent branching process in random environments. For the model where {Zn}n≥0 is associated with the stationary environment ξ− = {ξn}n≥0, let B = {ω : Zn(ω) = for some n}, and q(ξ−) = P(B | ξ−, Z0 = 1). The result is that P(q(̅ξ) = 1) is either 1 or 0, and sufficient conditions for certain extinction (i.e. P(q(ξ−) = 1) = 1) and for non-certain extinction (i.e. P(q(ξ−) < 1) = 1) are obtained for the model.
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2

Wang, Han-xing. "Extinction of population-size-dependent branching processes in random environments." Journal of Applied Probability 36, no. 01 (1999): 146–54. http://dx.doi.org/10.1017/s0021900200016922.

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Abstract:
We generalize a population-size-dependent branching process to a more general branching model called the population-size-dependent branching process in random environments. For the model where {Z n } n≥0 is associated with the stationary environment ξ− = {ξ n } n≥0, let B = {ω : Z n (ω) = for some n}, and q(ξ−) = P(B | ξ−, Z 0 = 1). The result is that P(q(̅ξ) = 1) is either 1 or 0, and sufficient conditions for certain extinction (i.e. P(q(ξ−) = 1) = 1) and for non-certain extinction (i.e. P(q(ξ−) < 1) = 1) are obtained for the model.
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3

Hueter, Irene. "Branching processes in generalized autoregressive conditional environments." Advances in Applied Probability 48, no. 4 (2016): 1211–34. http://dx.doi.org/10.1017/apr.2016.71.

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AbstractBranching processes in random environments have been widely studied and applied to population growth systems to model the spread of epidemics, infectious diseases, cancerous tumor growth, and social network traffic. However, Ebola virus, tuberculosis infections, and avian flu grow or change at rates that vary with time—at peak rates during pandemic time periods, while at low rates when near extinction. The branching processes in generalized autoregressive conditional environments we propose provide a novel approach to branching processes that allows for such time-varying random environ
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4

Jagers, Peter, Fima C. Klebaner, and Serik Sagitov. "Markovian paths to extinction." Advances in Applied Probability 39, no. 2 (2007): 569–87. http://dx.doi.org/10.1239/aap/1183667624.

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Subcritical Markov branching processes {Zt} die out sooner or later, say at time T < ∞. We give results for the path to extinction {ZuT, 0 ≤ u ≤ 1} that include its finite dimensional distributions and the asymptotic behaviour of xu−1ZuT, as Z0=x → ∞. The limit reflects an interplay of branching and extreme value theory. Then we consider the population on the verge of extinction, as modelled by ZT-u, u > 0, and show that as Z0= x → ∞ this process converges to a Markov process {Yu}, which we describe completely. Emphasis is on continuous time processes, those in discrete time displaying a
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5

Wang, Han-Xing, and Dafan Fang. "Asymptotic behaviour of population-size-dependent branching processes in Markovian random environments." Journal of Applied Probability 36, no. 2 (1999): 611–19. http://dx.doi.org/10.1239/jap/1032374477.

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A population-size-dependent branching process {Zn} is considered where the population's evolution is controlled by a Markovian environment process {ξn}. For this model, let mk,θ and be the mean and the variance respectively of the offspring distribution when the population size is k and a environment θ is given. Let B = {ω : Zn(ω) = 0 for some n} and q = P(B). The asymptotic behaviour of limnZn and is studied in the case where supθ|mk,θ − mθ| → 0 for some real numbers {mθ} such that infθmθ > 1. When the environmental sequence {ξn} is a irreducible positive recurrent Markov chain (particular
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6

Klebaner, Fima C. "Asymptotic behavior of near-critical multitype branching processes." Journal of Applied Probability 28, no. 3 (1991): 512–19. http://dx.doi.org/10.2307/3214487.

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Sufficient conditions for survival and extinction of multitype population-size-dependent branching processes in discrete time are obtained. Growth rates are determined on the set of divergence to infinity. The limiting distribution of a properly normalized process can be generalized gamma, normal or degenerate.
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7

Klebaner, Fima C. "Asymptotic behavior of near-critical multitype branching processes." Journal of Applied Probability 28, no. 03 (1991): 512–19. http://dx.doi.org/10.1017/s0021900200042376.

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Sufficient conditions for survival and extinction of multitype population-size-dependent branching processes in discrete time are obtained. Growth rates are determined on the set of divergence to infinity. The limiting distribution of a properly normalized process can be generalized gamma, normal or degenerate.
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8

Klebaner, F. C., and R. Liptser. "Likely path to extinction in simple branching models with large initial population." Journal of Applied Mathematics and Stochastic Analysis 2006 (May 14, 2006): 1–23. http://dx.doi.org/10.1155/jamsa/2006/60376.

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We give explicit formulae for most likely paths to extinction in simple branching models when initial population is large. In discrete time, we study the Galton-Watson process, and in continuous time, the branching diffusion. The most likely paths are found with the help of the large deviation principle (LDP). We also find asymptotics for the extinction probability, which gives a new expression in continuous time and recovers the known formula in discrete time. Due to the nonnegativity of the processes, the proof of LDP at the point of extinction uses a nonstandard argument of independent inte
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9

Hautphenne, S., G. Latouche, and G. Nguyen. "Extinction Probabilities of Branching Processes with Countably Infinitely Many Types." Advances in Applied Probability 45, no. 04 (2013): 1068–82. http://dx.doi.org/10.1017/s0001867800006777.

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We present two iterative methods for computing the global and partial extinction probability vectors for Galton-Watson processes with countably infinitely many types. The probabilistic interpretation of these methods involves truncated Galton-Watson processes with finite sets of types and modified progeny generating functions. In addition, we discuss the connection of the convergence norm of the mean progeny matrix with extinction criteria. Finally, we give a sufficient condition for a population to become extinct almost surely even though its population size explodes on the average, which is
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10

Hautphenne, S., G. Latouche, and G. Nguyen. "Extinction Probabilities of Branching Processes with Countably Infinitely Many Types." Advances in Applied Probability 45, no. 4 (2013): 1068–82. http://dx.doi.org/10.1239/aap/1386857858.

Full text
Abstract:
We present two iterative methods for computing the global and partial extinction probability vectors for Galton-Watson processes with countably infinitely many types. The probabilistic interpretation of these methods involves truncated Galton-Watson processes with finite sets of types and modified progeny generating functions. In addition, we discuss the connection of the convergence norm of the mean progeny matrix with extinction criteria. Finally, we give a sufficient condition for a population to become extinct almost surely even though its population size explodes on the average, which is
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