Annales de l'Institut Henri Poincaré, Probabilités et Statistiques

The many-to-few lemma and multiple spines

Simon C. Harris and Matthew I. Roberts

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Abstract

We develop a simple and intuitive identity for calculating expectations of weighted $k$-fold sums over particles in branching processes, generalising the well-known many-to-one lemma.

Résumé

On développe une identité simple et intuitive pour calculer l’espérance des sommations $k$-plier sur particules dans les processus de branchement, la généralisation du lemme bien connu ‘many-to-one’.

Article information

Source
Ann. Inst. H. Poincaré Probab. Statist., Volume 53, Number 1 (2017), 226-242.

Dates
Received: 11 September 2014
Revised: 8 September 2015
Accepted: 11 September 2015
First available in Project Euclid: 8 February 2017

Permanent link to this document
https://projecteuclid.org/euclid.aihp/1486544890

Digital Object Identifier
doi:10.1214/15-AIHP714

Mathematical Reviews number (MathSciNet)
MR3606740

Zentralblatt MATH identifier
1361.60076

Subjects
Primary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.)

Keywords
Branching processes Many-to-one Many-to-few Spine

Citation

Harris, Simon C.; Roberts, Matthew I. The many-to-few lemma and multiple spines. Ann. Inst. H. Poincaré Probab. Statist. 53 (2017), no. 1, 226--242. doi:10.1214/15-AIHP714. https://projecteuclid.org/euclid.aihp/1486544890


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