Prediction of the Intensity Process of Doubly Stochastic Multichannel Poisson Processes

Author

Fernández-Alcalá, Rosa María ; Navarro-Moreno, Jesús ; Ruiz-Molina, Juan Carlos

Author_Institution

Dept. of Stat. & Oper. Res., Univ. of Jaen, Jaen, Spain

Volume

57

Issue

7

fYear

2012

fDate

7/1/2012 12:00:00 AM

Firstpage

1843

Lastpage

1848

Abstract

This paper is concerned with the problem of predicting the intensity process of an observed doubly stochastic multichannel Poisson process. Under the only hypothesis that the covariance function of the intensity process is separable, recursive algorithms for the computation of the optimal linear filter and predictor are designed. Approximate solutions to the nonlinear filtering and prediction problems are also given. The main advantage of the proposed solutions is that they can be applied to those situations where the intensity process does not satisfy a stochastic differential equation.

Keywords

approximation theory; covariance analysis; nonlinear filters; prediction theory; stochastic processes; approximate solution; covariance function; intensity process; nonlinear filtering; observed doubly stochastic multichannel Poisson process; optimal linear filter; prediction problems; separable recursive algorithm; Approximation methods; Covariance matrix; Equations; Mathematical model; Prediction algorithms; Predictive models; Stochastic processes; Doubly stochastic multichannel Poisson processes; minimum mean square-error filtering and prediction problems;

fLanguage

English

Journal_Title

Automatic Control, IEEE Transactions on

Publisher

ieee

ISSN

0018-9286

Type

jour

DOI

10.1109/TAC.2011.2178878

Filename

6097032