持续转向Walker模型的渐近分析和扩散极限
Asymptotic analysis and diffusion limit of the Persistent Turning Walker Model
摘要：
持续转向步行模型（PTWM）是由Gautrais等人在数学生物学中引入的，用于鱼类运动的建模。它涉及一个非椭圆次椭圆扩散的非线性路径泛函。该扩散求解基于Ornstein-Uhlenbeck高斯过程的动力学Fokker-Planck方程。Degond & Motsch最近利用偏微分方程技术研究了该模型的长时间“扩散”行为。然而，这个模型本质上是概率性的。在本文中，我们将展示如何使用适当的工具，从随机分析，这个模型的长期扩散行为可以基本上恢复和扩展。该方法可以适用于许多其他的动力学“概率”模型。
英文摘要：
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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