Abstract
In a reinforced Galton–Watson process with reproduction law and memory parameter , the number of children of a typical individual either, with probability , repeats that of one of its forebears picked uniformly at random, or, with complementary probability , is given by an independent sample from . We estimate the average size of the population at a large generation, and in particular, we determine explicitly the Malthusian growth rate in terms of and . Our approach via the analysis of transport equations owes much to works by Flajolet and co‐authors.
| Item Type: | Journal Article, refereed, original work |
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| Communities & Collections: | 07 Faculty of Science > Institute of Mathematics |
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| Dewey Decimal Classification: | 510 Mathematics |
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| Scopus Subject Areas: | Physical Sciences > Software
Physical Sciences > General Mathematics
Physical Sciences > Computer Graphics and Computer-Aided Design
Physical Sciences > Applied Mathematics |
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| Uncontrolled Keywords: | Galton-Watson process, Malthusian growth exponent, singularity analysis of generating functions, stochastic reinforcement, transport equation
Research Areas, Computer Science, Mathematics
Computer Science, Software EngineeringMathematics, AppliedMathematics |
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| Language: | English |
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| Date: | 1 September 2024 |
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| Deposited On: | 09 May 2024 10:23 |
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| Last Modified: | 27 Feb 2025 02:44 |
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| Publisher: | Wiley-Blackwell Publishing, Inc. |
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| ISSN: | 1042-9832 |
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| Additional Information: | ACKNOWLEDGMENTS
We express our sincere gratitude to the reviewers for their insightful comments, which greatly contributed to enhancing the quality of this manuscript. J.B. would also like to thank KlausWidmayer for discussions about transport equations, and notably Lemma 3.3.
DATA AVAILABILITY STATEMENT
Data sharing not applicable to this article as no datasets were generated or analyzed during the
current study. |
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| OA Status: | Hybrid |
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| Publisher DOI: | https://doi.org/10.1002/rsa.21219 |
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Bertoin, Jean