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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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.


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

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

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

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


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.

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