Abbreviated title. Rare events in Markov chains. AMS 1991 subject classiications. 60J27. Abstract The distribution of waiting time until a rare event is often approximated by the exponential distribution. In the context of rst hitting times for stationary reversible chains, the error has a simple explicit bound involving only the mean waiting time ET and… (More)
A random walk that is skip-free to the left can only move down one level at a time but can skip up several levels. Such random walk features prominently in many places in applied probability including queuing theory and the theory of branching processes. This article exploits the special structure in this class of random walk to obtain a number of… (More)
A previous paper discussed explicit bounds in the exponential approximation for the distribution of the waiting time until a stationary reversible Markov chain rst enters a \rare" subset of states. In this paper Stein's method is used to get explicit (but complicated) bounds on the Poisson approximation for the number of non-adjacent visits to a rare subset.
We develop a systematic matrix-analytic approach, based on intertwinings of Markov semigroups, for proving theorems about hitting-time distributions for finite-state Markov chains—an approach that (sometimes) deepens understanding of the theorems by providing corresponding sample-path-by-sample-path stochastic constructions. We employ our approach to give… (More)
Globally, two bird–pollination systems have been recognised, involving specialist and occasional nectar-feeding birds. Whether avian pollinators place selective pressure on the plants they feed on, in terms of flower morphology and nectar traits, is still debated. While considerable research exists that examines the sugar preferences, concentration… (More)
The thermoregulatory capacity of a species can determine which climatic niche it occupies. Its development in avian chicks is influenced by numerous factors. Furthermore, it is suggested that altricial chicks develop their thermoregulatory capacity post-hatching, while precocial chicks develop aspects of this in the egg. We investigated the development of… (More)
There are two alternative hypotheses related to body size and competition for restricted food sources. The first one supposes that larger animals are superior competitors because of their increased feeding abilities, whereas the second one assumes superiority of smaller animals because of their lower food requirements. We examined the relationship between… (More)
Wild-caught animals are regularly used in physiological studies, yet the length of time it takes for completion of their acclimation to laboratory conditions remains largely unknown. In particular, Afrotropical species are relatively understudied compared with temperate and Holarctic species. Thus, we measured a number of metabolic variables in a 10g… (More)