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On the characteristic functional of a doubly stochastic Poisson process: Application to a narrow-band process |
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| Authors: | PR Bouzas MJ Valderrama AM Aguilera |
| Institution: | 1. Department of Statistic and Operations Research, Faculty of Pharmacy, Campus de Cartuja, University of Granada, 18071-Granada, Spain;2. Department of Statistic and Operations Research, Faculty of Sciences, University of Granada, 18071-Granada, Spain |
| Abstract: | 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. |
| Keywords: | Doubly stochastic Poisson process Characteristic functional Narrow band process Karhunen&ndash Loè ve expansion |
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