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Controlled Heterogeneous Collection: The Role of Occupation Numbers

Part of: Stochastic analysis Markov processes Stochastic systems and control

Published online by Cambridge University Press:  14 July 2016

A. Gerardi  and
P. Tardelli
A. Gerardi*
Affiliation:
Universitá dell'Aquila
P. Tardelli*
Affiliation:
Universitá dell'Aquila
*
∗Postal address: Dipartimento di Ingegneria Elettrica e dell'Informazione, Universitá dell'Aquila, 67040 Poggio di Roio, Italy.
∗Postal address: Dipartimento di Ingegneria Elettrica e dell'Informazione, Universitá dell'Aquila, 67040 Poggio di Roio, Italy.
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Abstract

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A controlled heterogeneous collection of identical items is presented. According to their level of wear and tear, they are divided into a finite number of classes and the partition of the collection is allowed to change over time. A suitable exchangeability assumption is made to preserve the property that the items be identical. The role of the occupation numbers is investigated and a filtering problem is set up, where the observation is the cardinality of a particular class. A control on the dynamics of the items is introduced, and the existence of an optimal control is proved. A discrete-time approximation for the separated problem, which is a finite-dimensional one, is performed. As a consequence, an approximation for the value function is given.

Keywords

Heterogeneous populationexchangeabilitystochastic filteringoptimal stochastic control

MSC classification

Secondary: 93E11: Filtering 93E20: Optimal stochastic control 60H30: Applications of stochastic analysis (to PDE, etc.) 60J75: Jump processes
Type
Research Article
Information
Journal of Applied Probability , Volume 45 , Issue 3 , September 2008 , pp. 595 - 609
Copyright
Copyright © Applied Probability Trust 2008 

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