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Heterogeneous population dynamical model: a filtering problem

Part of: Stochastic analysis Markov processes Stochastic systems and control Survival analysis and censored data Stochastic processes

Published online by Cambridge University Press:  14 July 2016

A. Gerardi  and
P. Tardelli
A. Gerardi*
Affiliation:
Università dell'Aquila
P. Tardelli*
Affiliation:
Università dell'Aquila
*
∗Postal address: Dipartimento di Ingegneria Elettrica, Facoltà di Ingegneria, Università dell'Aquila, Aquila, Italy.
∗Postal address: Dipartimento di Ingegneria Elettrica, Facoltà di Ingegneria, Università dell'Aquila, Aquila, Italy.
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Abstract

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We consider a heterogeneous population of identical particles divided into a finite number of classes according to their level of health. The partition can change over time, and a suitable exchangeability assumption is made to allow for having identical items of different types. The partition is not observed; we only observe the cardinality of a particular class. We discuss the problem of finding the conditional distribution of particle lifetimes, given such observations, using stochastic filtering techniques. In particular, a discrete-time approximation is given.

Keywords

Heterogeneous populationexchangeabilitystochastic filtering

MSC classification

Primary: 62N05: Reliability and life testing
Secondary: 93E11: Filtering 60H30: Applications of stochastic analysis (to PDE, etc.) 60G35: Signal detection and filtering 60J75: Jump processes
Type
Research Papers
Information
Journal of Applied Probability , Volume 42 , Issue 2 , June 2005 , pp. 346 - 361
Copyright
© Applied Probability Trust 2005 

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