Let be a complete separable metric space and (Fn)n[greater-or-equal, slanted]0 a sequence of i.i.d. random functions from to which are uniform Lipschitz, that is, Ln=supx[not equal to]y d(Fn(x),Fn(y))/d(x,y)[infinity] a.s. Providing the mean contraction assumption and for some , it was proved by...

Lam and Lehoczky (1991) have recently given a number of extensions of classical renewal theorems to superpositions of p independent renewal processes. In this article we want to advertise an approach that more explicitly uses a Markov renewal theoretic framework and thus leads to a simplified...

Let (S, £) be a measurable space with countably generated [sigma]-field £ and (Mn, Xn)n[greater-or-equal, slanted]0 a Markov chain with state space S x and transition kernel :S x ( [circle times operator] )--[0, 1]. Then (Mn,Sn)n[greater-or-equal, slanted]0, where Sn = X0+...+Xn for...

This article continues work by Alsmeyer and Hoefs (Markov Process Relat. Fields 7 (2001) 325-348) on random walks (Sn)n[greater-or-equal, slanted]0 whose increments Xn are (m+1)-block factors of the form [phi](Yn-m,...,Yn) for i.i.d. random variables Y-m,Y-m+1,... taking values in an arbitrary...

Let X1, X2,..., be i.i.d. random variables, whose distribution function is continuous and set Yn = max{X1, X2,..., Xn}, n [greater-or-equal, slanted] 1. We provide elementary proofs of some results on the set of limit points of Yn.

The waiting times in certain multinomial experiments are studied. Special cases are the waiting times in a roulette game and in some dice problems sought for earlier. The main ingredients are the theory of stopped sums and an alternative formulation using independent Poisson processes.

Much of this author's work has been devoted to stopped random walks with applications to renewal theory etc. Some results have earlier been generalized to Lévy processes. The purpose of the present paper is to present some further generalizations of this kind.

This note is devoted to the connection between a theorem due to Gnedenko, classical central limit theory, and the weak law of large numbers.

Limit theorems for stopped two-dimensional random walks are generalized to perturbed random walks and perturbed Lévy processes. We conclude with an application to repeated significance tests in two-parameter exponential families and an example.