Ergodicity and inequalities in a class of point processes

Torgny Lindvall

Stochastic Processes and their Applications, 1988, vol. 30, issue 1, 121-131

Abstract: In this paper we extend some results from renewal theory to a certain class of point processes. Firstly, a strong version of Blackwell's renewal theorem is shown to hold when the memory of the process at time t, say, contains only the configuration of the latest m points of occurrence preceding t, and of the points in the interval [t-A,t], where A is a constant. Secondly, a generalization of the decreasing failure rate (DFR) concept is introduced, based on the following principle: "if there have been many points of occurrence recently, then we will soon experience another one". Inequalities and monotonicity results are established under this new type of DFR assumption.

Keywords: coupling; imbedding; in; a; bivariate; Poisson; process; renewal; theorem; DFR; inequalities; monotonicity (search for similar items in EconPapers)
Date: 1988
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Citations: View citations in EconPapers (3)

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