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Pré-Publication, Document De Travail Année : 2022

Asymptotic behaviour of a one-dimensional avalanche model through a particular stochastic process

Résumé

In this paper we develop the study of a binary coagulation-fragmentation equation which describes the avalanches phenomena. We construct first an adapted stochastic process and obtain its behaviour to the equilibrium. Our model is based on self-organized critical (SOC) systems and in particular on a simple sand pile model introduced in Bressaud and Fournier, [BrFo 09]. Furthermore, we define a stochastic differential equation for this process and propose a numerical method in order to approximate the solution. The key point of our work is a new interpretation of the avalanches phenomena by handling stochastic differential equations with jumps and the analysis of the invariant behaviour of the stochastic process.
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Dates et versions

hal-03947249 , version 1 (19-01-2023)

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  • HAL Id : hal-03947249 , version 1

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Madalina Deaconu, Oana Lupaşcu-Stamate. Asymptotic behaviour of a one-dimensional avalanche model through a particular stochastic process. 2022. ⟨hal-03947249⟩
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