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Conditional law of a branching process observing a subpopulation

Part of: Markov processes Stochastic systems and control

Published online by Cambridge University Press:  14 July 2016

Claudia Ceci  and
Anna Gerardi
Claudia Ceci*
Affiliation:
Università di Chieti
Anna Gerardi*
Affiliation:
Università dell’Aquila
*
∗ Postal address: Dipartimento di Scienze, Facoltà di Economia, Università di Chieti, 65127 Pescara, Italy.
∗∗ Postal address: Dipartimento di Ingegneria Elettrica, Facoltà di Ingegneria, Università dell’Aquila, L’Aquila, Italy. Email address: gerardi@ing.univaq.it
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Abstract

The paper is concerned with filtering the cardinality of a branching process observing the cardinality of a subpopulation. In this model, both the processes, state and observation are pure jump processes and may have common jump times. Preliminary properties are studied in the tree framework. A recursive structure for the filtering equation is proved in the supercritical case.

Keywords

Branching processesmarked treesfiltering

MSC classification

Primary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.)
Secondary: 60J75: Jump processes 93E11: Filtering
Type
Research Papers
Information
Journal of Applied Probability , Volume 39 , Issue 1 , March 2002 , pp. 112 - 122
Copyright
Copyright © Applied Probability Trust 2002 

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