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Conditional Poisson processes

Published online by Cambridge University Press:  14 July 2016

Richard F. Serfozo
Richard F. Serfozo*
Affiliation:
Syracuse University
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Abstract

A conditional Poisson process (often called a double stochastic Poisson process) is characterized as a random time transformation of a Poisson process with unit intensity. This characterization is used to exhibit the jump times and sizes of these processes, and to study their limiting behavior. A conditional Poisson process, whose intensity is a function of a Markov process, is discussed. Results similar to those presented can be obtained for any process with conditional stationary independent increments.

Keywords

POISSON PROCESSESRANDOM TIME TRANSFORMATIONSLIMIT THEOREMSRANDOM ENVIRONMENTSCONDITIONAL STATIONARY INDEPENDENT INCREMENTSMARKOV ENVIRONMENTSDOUBLE STOCHASTICPOINT PROCESSMARKOV ADDITIVE PROCESS
Type
Research Papers
Information
Journal of Applied Probability , Volume 9 , Issue 2 , June 1972 , pp. 288 - 302
Copyright
Copyright © Applied Probability Trust 1972 

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