15 Result(s)
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Article
Anthony G. Pakes
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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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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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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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Necessary conditions for characterization of laws via mixed sums
SupposeX andY are independent and identically distributed, and independent ofU which satisfies 0≤U≤1. Recent work has centered on finding the lawsL(X) for whichX ℞U(X+Y) where ℞ denotes equality in law. We show t...
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Characterizations, length-biasing, and infinite divisibility
SupposeL(X) is the law of a positive random variableX, andZ is positive and independent ofX. Admissible solution pairs (L(X),L(Z)) are sought for the in-law equation
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Characterization of laws by balancing weighting against a binary operation
LetL(X) be the law of a positive random variableX, andZ be positive and independent ofX. Solution pairs (L(X), L(Z)) are sought for the in-law equation ...
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Extreme order statistics on Galton-Watson trees
This paper studies the asymptotic behaviour of extreme order statistics of i.i.d. random scores ascribed to each individual in a Galton-Watson family tree. Of interest is the asymptotic behaviour of the order ...
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Criteria for Convergence of the Number of Near Maxima for Long Tails
Let M n denote the maximum of a random sample of size n and K n (a) be the number of near maxima, i.e. the number of sample observations in the...
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Limit theorems for numbers of near-records
Observations occurring between successive record times and within a distance a > 0 of the current record value are called near-records. Limit theorems for the number ξ n
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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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Some properties of the exponential distribution class with applications to risk theory
This paper derives some equivalent conditions for tail equivalence of a distribution G and the convolution G*H, where G belongs to the exponential distribution class and H is another distribution. This generalize...
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Limit theorems for record counts and times in the F α -scheme
We determine the almost sure and central limiting behaviour of the number of records and record times for the F α -scheme. Elementary methods are used to obtain ...
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On relative stability and weighted laws of large numbers
Weighted laws of large numbers are established for components which are independent copies of a positive relatively stable law and the weights comprise a regularly varying sequence. The index of regular variat...
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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...
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Open AccessStructural properties of generalised Planck distributions
A family of generalised Planck (GP) laws is defined and its structural properties explored. Sometimes subject to parameter restrictions, a GP law is a randomly scaled gamma law; it arises as the equilibrium la...
