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Journal Articles Probability Surveys Year : 2023

Probabilistic representations of fragmentation equations

Abstract

In this survey article, we present various probabilistic representations of the fragmentation equation, and show how they are related. We focus on the stochastic process which represents the evolution of the mass of a typical particle subjected to a fragmentation process. These probabilistic representations range from Markov chains to Stochastic Differential Equations with jumps, and we consider how they are interrelated. In particular, we show how these representations leads to easy numerical simulations.
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Dates and versions

hal-03483448 , version 1 (16-12-2021)
hal-03483448 , version 2 (25-11-2022)
hal-03483448 , version 3 (03-03-2023)
hal-03483448 , version 4 (13-03-2023)

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Madalina Deaconu, Antoine Lejay. Probabilistic representations of fragmentation equations. Probability Surveys, 2023, 20, pp.226-290. ⟨10.1214/23-PS14⟩. ⟨hal-03483448v4⟩
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