Nadjia El Saadi ; Ovide Arino - A stochastic modelling of phytoplankton aggregation

arima:1856 - Revue Africaine de Recherche en Informatique et Mathématiques Appliquées, November 5, 2006, Volume 5, Special Issue TAM TAM'05, november 2006 -
A stochastic modelling of phytoplankton aggregation

Authors: Nadjia El Saadi 1; Ovide Arino 1

  • 1 Institut de Recherche pour le Développement

The aim of this work is to provide a stochastic mathematical model of aggregation in phytoplankton, from the point of view of modelling a system of a large but finite number of phytoplankton cells that are subject to random dispersal, mutual interactions allowing the cell motions some dependence and branching (cell division or death). We present the passage from the ''microscopic'' description to the ''macroscopic'' one, when the initial number of cells tends to infinity (large phytoplankton populations). The limit of the system is an extension of the Dawson-Watanabe superprocess: it is a superprocess with spatial interactions which can be described by a nonlinear stochastic partial differential equation.

Volume: Volume 5, Special Issue TAM TAM'05, november 2006
Published on: November 5, 2006
Submitted on: April 11, 2006
Keywords: Phytoplankton aggregation, Lagrangian model, Interacting branching diffusion process, Martingale problem, Weak convergence, Dawson-Watanabe superprocess, Stochastic partial differential equation,Agrégation du phytoplancton,Modèle Lagrangien,Processus de branchement diffusion interactif,Problème de martingales,Convergence faible,Superprocessus de Dawson-Watanabe,Equation aux dérivées partielles stochastique,[MATH] Mathematics [math],[INFO] Computer Science [cs]

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