ON THE DISTRIBUTION OF A RANDOMLY DISCOUNTED COMPOUND POISSON-PROCESS

Authors
NILSEN T PAULSEN J
Citation
T. Nilsen et J. Paulsen, ON THE DISTRIBUTION OF A RANDOMLY DISCOUNTED COMPOUND POISSON-PROCESS, Stochastic processes and their applications, 61(2), 1996, pp. 305-310
Citations number
6
Categorie Soggetti
Statistic & Probability","Statistic & Probability
Journal title
Stochastic processes and their applications → ACNP
ISSN journal
03044149
Volume
61
Issue
2
Year of publication
1996
Pages
305 - 310
Database
ISI
SICI code
0304-4149(1996)61:2<305:OTDOAR>2.0.ZU;2-9
Abstract
We study the distribution of the stochastic integral integral(0)(infin ity) e(-Rt) dP(t) where R is a Brownian motion with positive drift and P is an independent compound Poisson process. We show that in the spe cial case when the jumps of P are exponentially distributed, the integ ral has the same distribution as that of a gamma variable divided by a n independent beta variable.