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Multitype branching processes observing particles of a given type

Part of: Stochastic systems and control Markov processes

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

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A multitype branching process is presented in the framework of marked trees and its structure is studied by applying the strong branching property. In particular, the Markov property and the expression for the generator are derived for the process whose components are the numbers of particles of each type. The filtering of the whole population, observing the number of particles of a given type, is discussed. Weak uniqueness for the filtering equation and a recursive structure for the linearized filtering equation are proved under a suitable assumption on the reproduction law.

Keywords

Branching processmarked treefiltering

MSC classification

Primary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.)
Secondary: 60J75: Jump processes 93E11: Filtering

Information

Type
Research Papers
Information
Journal of Applied Probability , Volume 42 , Issue 2 , June 2005 , pp. 446 - 462
Copyright
© Applied Probability Trust 2005 

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