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Processes with conditional stationary independent increments

Published online by Cambridge University Press:  14 July 2016

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

We study a class of processes which are essentially processes with stationary independent increments whose basic parameters are allowed to vary randomly over time. These processes are equivalent to random time transformations of processes with stationary independent increments where the time process is independent of the original process. Several limiting theorems are presented including weak and strong laws of large numbers and a functional central limit theorem.

Keywords

PROCESSES WITH STATIONARY INDEPENDENT INCREMENTSPOISSON PROCESSWIENER PROCESSRANDOM TIME TRANSFORMATIONERGODIC THEOREMSFUNCTIONAL CENTRAL LIMIT THEOREM

Information

Type
Research Papers
Information
Journal of Applied Probability , Volume 9 , Issue 2 , June 1972 , pp. 303 - 315
Copyright
Copyright © Applied Probability Trust 1972 

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