7 Result(s)
within
Anthony G. Pakes
Mathematics
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Article
Limit theorems for the population size of a birth and death process allowing catastrophes
The linear birth and death process with catastrophes is formulated as a right continuous random walk on the non-negative integers which evolves in continuous time with an instantaneous jump rate proportional t...
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Article
The supercritical birth, death and catastrophe process: Limit theorems on the set of non-extinction
The skip-free property of the super-critical linear birth and death process with a linear catastrophe component is exploited to obtain an almost sure convergence theorem for the population size without any ext...
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Chapter
Legumes at Loggerheads: Modelling Competition Between Two Strains of Sub-Clover
In essence this paper is a précis of a substantial investigation of deterministic modelling of two strains of sub-clover which interact competitively at the time they set their seed.
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Article
On family trees and subtrees of simple branching processes
We study the probability of occurrence of certain subtrees of the family tree of a Galton Watson branching process.
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Chapter
On the Recognition and Structure of Probability Generating Functions
If $$ M\left( s \right) = 1 - {e^{ - \pi (s)}} $$ is a probability generating function, the coefficients π j in the MacLaurin e...
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Article
Asymptotic Properties of the Markov Branching Process with Immigration
We consider the Markov branching process with immigration allowing the possibility of infinite numbers of offspring and/or immigrants. Our focus is on the construction and uniqueness of the minimal transition ...
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Article
Self-Decomposable Laws from Continuous Branching Processes
The martingale limit law of the supercritical continuous time and state branching process either is compound Poisson or self-decomposable. This paper explores some general aspects of the latter case. A fundame...
