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
139-145
Jones, Owen Dafydd
00ea4a6b-0a5f-4d87-8c3c-c417056211fb
1999
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), .
(doi:10.1239/jap/1032374236).
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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Published date: 1999
Keywords:
branching process, multi-type, varying environment, continuity
Organisations:
Operational Research
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Local EPrints ID: 29682
URI: http://eprints.soton.ac.uk/id/eprint/29682
ISSN: 0021-9002
PURE UUID: 04a64b5f-be9a-47f4-8c2b-88a174864b17
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Date deposited: 02 May 2007
Last modified: 15 Mar 2024 07:33
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Author:
Owen Dafydd Jones
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