A strong law of large numbers for branching processes: almost sure spine events

Simon C Harris; Matthew I Roberts

doi:10.1214/ECP.v19-2641

A strong law of large numbers for branching processes: almost sure spine events

Simon C Harris, Matthew I Roberts

Research output: Contribution to journal › Article › peer-review

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Abstract

We demonstrate a novel strong law of large numbers for branching processes, with a simple proof via measure-theoretic manipulations and spine theory. Roughly speaking, any sequence of events that eventually occurs almost surely for the spine entails the almost sure convergence of a certain sum over particles in the population.

Original language	English
Article number	28
Pages (from-to)	1-6
Number of pages	6
Journal	Electronic Communications in Probability
Volume	19
DOIs	https://doi.org/10.1214/ECP.v19-2641
Publication status	Published - 8 May 2014

Keywords

Branching processes
Strong law of large numbers
Spine

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10.1214/ECP.v19-2641

2641-17176-1-PBFinal published version, 196 KBLicence: CC BY

Cite this

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title = "A strong law of large numbers for branching processes: almost sure spine events",

abstract = "We demonstrate a novel strong law of large numbers for branching processes, with a simple proof via measure-theoretic manipulations and spine theory. Roughly speaking, any sequence of events that eventually occurs almost surely for the spine entails the almost sure convergence of a certain sum over particles in the population.",

keywords = "Branching processes, Strong law of large numbers, Spine",

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AU - Roberts, Matthew I

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AB - We demonstrate a novel strong law of large numbers for branching processes, with a simple proof via measure-theoretic manipulations and spine theory. Roughly speaking, any sequence of events that eventually occurs almost surely for the spine entails the almost sure convergence of a certain sum over particles in the population.

KW - Branching processes

KW - Strong law of large numbers

KW - Spine

UR - http://dx.doi.org/10.1214/ECP.v19-2641

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DO - 10.1214/ECP.v19-2641

M3 - Article

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JO - Electronic Communications in Probability

JF - Electronic Communications in Probability

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ER -

A strong law of large numbers for branching processes: almost sure spine events

Abstract

Keywords

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EPSRC Posdoctoral Fellowship in Applied Probability for Dr Matthew I Roberts

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A strong law of large numbers for branching processes: almost sure spine events

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Projects

EPSRC Posdoctoral Fellowship in Applied Probability for Dr Matthew I Roberts

Cite this