We consider how to choose the reproduction rates in a one-dimensional contact process on a finite set to maximize the growth rate of the extinction time with the population size. The constraints are an upper bound on the average reproduction rate, and that the rate profile must be piecewise...

In this paper we derive an alternative representation for the reflection of a continuous, bounded variation process. Under stationarity assumptions we prove a continuous counterpart of Little's law of classical queueing theory. These results, together with formulas from Palm calculus, are used...

Based on recent results on the exploitation of "drift criteria" for general state-space Markov processes, we derive rates of convergence for (moments of ) processes associated with a renewal process with common inter-renewal time distribution F. Some of the results are classical and some are...

Ballot theorems yield a simple relation for the probability that a non-decreasing process with cyclically interchangeable increments and piecewise constant paths stay below a linear function for a certain period of time. A particular instance of the problem is the classical ballot theorem that...