Asymptotic analysis and diffusion limit of the Persistent Turning Walker Model

Details Asymptotic analysis and diffusion limit of the Persistent Turning Walker Model Asymptotic analysis and diffusion limit of the Persistent Turning Walker Model

2008-11-04

arxiv.org/abs/0811.0600v2

Asymptotic Analysis 67, 17-31 (2010)

Mathematics

Analysis of PDEs

Accepted for publication in Asymptotic Analysis

Scientific paper

10.3233/ASY-2009-0969

The Persistent Turning Walker Model (PTWM) was introduced by Gautrais et al in Mathematical Biology for the modelling of fish motion. It involves a nonlinear pathwise functional of a non-elliptic hypo-elliptic diffusion. This diffusion solves a kinetic Fokker-Planck equation based on an Ornstein-Uhlenbeck Gaussian process. The long time "diffusive" behavior of this model was recently studied by Degond & Motsch using partial differential equations techniques. This model is however intrinsically probabilistic. In the present paper, we show how the long time diffusive behavior of this model can be essentially recovered and extended by using appropriate tools from stochastic analysis. The approach can be adapted to many other kinetic "probabilistic" models.

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