Convergence of thinning processes using compensators (Q1086912)

For each \(n=1,2,..\). let \(\eta_ n\) be a simple point process with possible points only at the positive integers: \(\eta_ n=\sum^{\infty}_{j=1}X_{nj}\delta_ j\), where the \(X_{nj}'s\) are (dependent) 0-1 random variables. Using the compensation approach, the paper gives, for various types of such processes, thinning conditions implying the convergence of suitable scalings \(\eta_ ng_ n^{-1}\) to a Poisson process with rate 1. The types in question are 0-1 Markov chains with nonstationary transition probabilities, 2-dependent stationary Markov chains, the times of success runs in Bernoulli processes and the times of high level exceedances in stationary processes.