On the characteristic functional of a doubly stochastic Poisson process: Application to a narrow-band process
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Doubly stochastic Poisson processCharacteristic functionalNarrow band processKarhunen–Loève expansion
P.R. Bouzas, M.J. Valderrama, A.M. Aguilera, On the characteristic functional of a doubly stochastic Poisson process: Application to a narrow-band process, Applied Mathematical Modelling, Volume 30, Issue 9, 2006, Pages 1021-1032, ISSN 0307-904X, https://doi.org/10.1016/j.apm.2005.07.005
SponsorshipProject MTM2004-05992 of Dirección General de Investigación, Ministerio de Ciencia y Tecnologıía
The characteristic functional (c.fl.) of a doubly stochastic Poisson process (DSPP) is studied and it provides us the finite dimensional distributions of the process and so its moments. It is also studied the case of a DSPP which intensity is a narrow-band process. The Karhunen–Loève expansion of its intensity is used to obtain the probability distribution function and a decomposition of this Poisson process. The covariance derived from the general c.fl. is applied in this particular DSPP.