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Journal Articles Foundations of Data Science Year : 2023

Diagnostic of the Lévy area for geophysical flow models in view of defining high order stochastic discrete-time schemes

Diagnostic of the Lévy area for geophysical flow models in view of defining high order stochastic discrete-time schemes

Abstract

In this paper we characterize numerically through two criteria the Lévy area related to unresolved fluctuation velocities associated to a stochastic coarse-scale representation of geophysical fluid flow dynamics. We study in particular whether or not the process associated to the random unresolved velocity components exhibits a Lévy area corresponding to a Wiener process, and if the law of this process can reasonably be approached by a centered Dirac measure. This exploration enables us to answer positively to a conjecture made for the constitution of high-order discrete time evolution schemes for stochastic representation defined from stochastic transport.
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hal-04241686 , version 1 (13-10-2023)

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Pierre-Marie Boulvard, Etienne Mémin. Diagnostic of the Lévy area for geophysical flow models in view of defining high order stochastic discrete-time schemes. Foundations of Data Science, In press, pp.1-25. ⟨10.3934/fods.2023011⟩. ⟨hal-04241686⟩
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