The objective of this research has been to characterize in terms of spectral representations and interval distributions the univariate point process resulting from the superposition of a finite number of independent, identically distributed renewal processes with either Erlang or hyperexponential interval distributions. A corollary to the direct line of inquiry has involved a broad class of univariate point processes known as semi-Markov generated point processes . A semi-Markov generated point process may be thought of as a superposition of dependent renewal processes. The spectral and distributional characteristics are developed for such processes with finite state space, and the superposition of renewal processes with Erlang or hyperexponential interval distributions is shown to have an equivalent representation as a semi-Markov generated point process. Equivalence here refers to the probabalistic structure of the time between events, and more specifically, the spectral properties.

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http://archive.org/details/semimarkovgenera1094517227

Lieutenant Commander, United States Navy