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Continuity for multi-type branching processes with varying environments

Continuity for multi-type branching processes with varying environments
Continuity for multi-type branching processes with varying environments
Conditions are derived for the components of the normed limit of a multi-type branching process with varying environments, to be continuous on (0, ?). The main tool is an inequality for the concentration function of sums of independent random variables, due originally to Petrov. Using this, we show that if there is a discontinuity present, then a particular linear combination of the population types must converge to a non-random constant (Equation (1)). Ensuring this can not happen provides the desired continuity conditions.
branching process, multi-type, varying environment, continuity
0021-9002
139-145
Jones, Owen Dafydd
00ea4a6b-0a5f-4d87-8c3c-c417056211fb
Jones, Owen Dafydd
00ea4a6b-0a5f-4d87-8c3c-c417056211fb

Jones, Owen Dafydd (1999) Continuity for multi-type branching processes with varying environments. Journal of Applied Probability, 36 (1), 139-145. (doi:10.1239/jap/1032374236).

Record type: Article

Abstract

Conditions are derived for the components of the normed limit of a multi-type branching process with varying environments, to be continuous on (0, ?). The main tool is an inequality for the concentration function of sums of independent random variables, due originally to Petrov. Using this, we show that if there is a discontinuity present, then a particular linear combination of the population types must converge to a non-random constant (Equation (1)). Ensuring this can not happen provides the desired continuity conditions.

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More information

Published date: 1999
Keywords: branching process, multi-type, varying environment, continuity
Organisations: Operational Research

Identifiers

Local EPrints ID: 29682
URI: http://eprints.soton.ac.uk/id/eprint/29682
ISSN: 0021-9002
PURE UUID: 04a64b5f-be9a-47f4-8c2b-88a174864b17

Catalogue record

Date deposited: 02 May 2007
Last modified: 15 Jul 2019 19:08

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