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Integrals of branching processes
Biometrika, 1967SUMMARY For age-dependent branching processes X(t) integrals of the type Y(t) = f X(s) ds are studied. These may be looked upon as a measure of the amount of toxins produced in time (0, t) by a colony of bacteria. An integral equation for the moment generating function of {X(t), Y(t)} is deduced and used to analyze the asymptotic behaviour of the two ...
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Computerization of the branching process
Behavioral Science, 1967The branching process had its origin in Galton's curiosity about the extinction of family names; the mathematics developed for this original purpose has since found many applications in physical as well as social science. The present paper gives an elementary summary of the theory in the iterated function first developed, and then translates this ...
N, Keyfitz, A, Tyree
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The branching process with logistic growth
Annals of Applied Probability, 2005 In order to model random density-dependence in population dynamics, we construct the random analogue of the well-known logistic process in the branching processes ’ framework.
Amaury Lambert
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Probability in the Engineering and Informational Sciences, 1988
A set of niarms of typei, i= 1,…, L, is available. A pull of arm of typeioccupies a duration Viat the end of which a reward Ciand Ni1,…, NiLnew arms are obtained, while all other arms are frozen. A Gittins priority order of types is obtained and shown to yield the maximal discounted reward from this branching process of arms.
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A set of niarms of typei, i= 1,…, L, is available. A pull of arm of typeioccupies a duration Viat the end of which a reward Ciand Ni1,…, NiLnew arms are obtained, while all other arms are frozen. A Gittins priority order of types is obtained and shown to yield the maximal discounted reward from this branching process of arms.
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The Markov branching-castastrophe process
Stochastic Processes and Their Applications, 1986 This paper considers a Markov branching process modified to allow decrements which occur randomly at a rate proportional to the population size. The problems considered are (i) Conditions for eventual extinction, (ii) Asymptotic behaviour of the ...
Pakes, Anthony G.
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On an Explosive Branching Process
Theory of Probability & Its Applications, 1996Summary: We consider a Markov branching process \(\{Z(t)\), \(t \in [0, \tau)\}\) that explodes at a random time \(\tau\). [This means that \(P\{Z(t)=\infty \}>0\) for some \(t\in (0,\infty)\), and \(\tau:=\inf \{t:Z(t)=\infty \}\)]. We estimate the value of \(Z(t)\) for \(t\) close to \(\tau\).
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Branching processes with random absorbing processes
Journal of Applied Probability, 1978A discrete Galton–Watson process is modified by an absorbing process, which, within each generation, eliminates a subset of the living particles without leaving offspring. The absorbing process will be only roughly specified by its expected efficiency on the associated process.
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On the Convergence of Branching Processes to a Diffusion Process
Theory of Probability & Its Applications, 1986Translation from Teor. Veroyatn. Primen. 30, No.3, 468-477 (Russian) (1985; Zbl 0572.60085).
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On a Class of Branching Processes
Theory of Probability & Its Applications, 1975Ezhov, I. I., Shakhbazov, A. A.
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