Note on Superposition of Renewal Processes
Abstract: In this paper we
discuss distributional properties of superposition of renewal processes.
Firstly, as a special case, we discuss probability distributions of a
superposition of Poisson processes and its generalization, namely the sum of
independent compound Poisson processes. In this case we have explicit
expressions for their probability distributions. Secondly, we discuss the
statistical moments of general superposition of renewal processes. We also discuss
the statistical moments of the sum of independent renewal reward processes, a
generalization of a supervision of renewal processes. The results are presented
in the form of Laplace transforms. Finally we present the distributions of
recurrence times of a superposition of renewal processes.
Keywords: Poisson process,
Compound Poisson process, Renewal process, Renewal reward process, Laplace transform
Author: Suyono and J.A.M. van
der Weide
Kode Jurnal: jpmatematikagg100001
