Representations are found for a limit law L(Z(k,p)) obtained from an expanding sequence of random forests containing n nodes with p∈(0,1] a probability controlling bond formation. One implies that Z(k,p) is stochastically decreasing as k increases and that norming gives an exponential limit...

Let (Zt) be a subordinator independent of 0 = U = 1 and let u and v be positive constants. Solutions to the "in law" equation Zu = dUZu+v exist under certain conditions and they have a distribution function which is continuous on the positive reals. A discrete version of this equation is here...

The concept of a limiting conditional age distribution of a continuous time Markov process whose state space is the set of non-negative integers and for which {0} is absorbing is defined as the weak limit as t--[infinity] of the last time before t an associated "return" Markov process exited...

A Markov branching process with instantaneous immigration from the zero state can be constructed so as to be honest and have the non-negative integers as state-space, but the construction requires the branching part to be explosive. We show that a realistic model can be constructed without this...

This paper offers a simple proof based on random variable representations for a mixture representation of symmetric Linnik laws previously derived by purely analytic means. The new approach can be set in a much more general context which embraces the symmetric and the positive generalized Linnik...

Strong convergence, and a weak limit theorem, are obtained for a scheme of 'renormalized' order statistics whose distribution functions are defined by a scheme of functional iteration.

Given a sequence of i.i.d. random variables, new proofs are given for limit theorems for the number of observations near the maximum up to time n, as n -- [infinity]. The proofs rely on a Poisson approximation to conditioned binomial laws, and they reveal the origin in the limit laws of mixing...

In this paper we discuss the asymptotic behaviour of random contractions $X=RS$, where $R$, with distribution function $F$, is a positive random variable independent of $S\in (0,1)$. Random contractions appear naturally in insurance and finance. Our principal contribution is the derivation of...