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Strong laws of large numbers for a growth-fragmentation process with bounded cell sizes

Watson, Alexander; Horton, Emma; (2022) Strong laws of large numbers for a growth-fragmentation process with bounded cell sizes. ALEA: Latin American Journal of Probability and Mathematical Statistics (In press). Green open access

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Abstract

Growth-fragmentation processes model systems of cells that grow continuously over time and then fragment into smaller pieces. Typically, on average, the number of cells in the system exhibits asynchronous exponential growth and, upon compensating for this, the distribution of cell sizes converges to an asymptotic profile. However, the long-term stochastic behaviour of the system is more delicate, and its almost sure asymptotics have been so far largely unexplored. In this article, we study a growth-fragmentation process whose cell sizes are bounded above, and prove for the first time the existence of regimes with differing almost sure long-term behaviour.

Type: Article
Title: Strong laws of large numbers for a growth-fragmentation process with bounded cell sizes
Open access status: An open access version is available from UCL Discovery
Publisher version: https://alea.impa.br/english/index_v18.htm
Language: English
Additional information: This version is the author accepted manuscript. For information on re-use, please refer to the publisher's terms and conditions.
Keywords: Growth-fragmentation, law of large numbers, asynchronous exponential growth, cell division, ergodic theorem, spectral radius, spectral gap, intrinsic martingale, spectrally negative Lévy process, dividend process, skeleton decomposition
UCL classification: UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Statistical Science
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL
URI: https://discovery.ucl.ac.uk/id/eprint/10150803
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