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A central limit theorem for conservative fragmentation chains
Published online by Cambridge University Press: 17 March 2023
Abstract
We are interested in a fragmentation process. We observe fragments frozen when their sizes are less than $\varepsilon$ ($\varepsilon>0$). It is known (Bertoin and Martínez, 2005) that the empirical measure of these fragments converges in law, under some renormalization. Hoffmann and Krell (2011) showed a bound for the rate of convergence. Here, we show a central limit theorem, under some assumptions. This gives us an exact rate of convergence.
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- © The Author(s), 2023. Published by Cambridge University Press on behalf of Applied Probability Trust