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April, 1972 A Note on Poisson-Subordination
Jozef L. Teugels
Ann. Math. Statist. 43(2): 676-680 (April, 1972). DOI: 10.1214/aoms/1177692653


Pseudo-Poisson processes can be obtained from discrete time Markov processes by subordination. A continuous time analogue of a random walk is defined by $Y(t) = S\lbrack T(t)\rbrack$ where $S(n)$ is the partial sum of a sequence of independent identically distributed random variables and $T(t)$ a process with stationary independent increments, independent of $S(n)$ and taking values in the non-negative integers. It is then shown that $Y(t)$ is a compound Poisson process; furthermore the supremum of $Y(t)$ is Poisson-subordinated to the maximum of $S(n)$ if and only if $T(t)$ is a Poisson process.


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Jozef L. Teugels. "A Note on Poisson-Subordination." Ann. Math. Statist. 43 (2) 676 - 680, April, 1972.


Published: April, 1972
First available in Project Euclid: 27 April 2007

zbMATH: 0238.60096
MathSciNet: MR298765
Digital Object Identifier: 10.1214/aoms/1177692653

Rights: Copyright © 1972 Institute of Mathematical Statistics


Vol.43 • No. 2 • April, 1972
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