Stochastic modelling and analysis of spatio-temporal processes with fractal characteristics

近年来，人们对用分形模型来表示多孔介质中的扩散和输运、海洋和大气湍流、气候学等物理现象越来越感兴趣。本项目主要研究多重分形几何域上的扩散现象。分形谐波分析的最新进展和我们自己的分数阶广义随机场的发展使我们能够制定一个综合的方案来解决一些关键问题，包括分数阶扩散的建模、处理和统计估计。这一计划的进展将反过来有利于相关科学领域的发展。

Interest has grown in recent years on the derivation of fractal models to represent certain physical phenomena such as diffusion and transport in porous media, oceanic and atmospheric turbulence, climatology, etc. This project focuses on the phenomenon of diffusion on domains with multifractal geometry. Recent advances in harmonic analysis on fractals and our own development of fractional generalized random fields allow us to formulate a comprehensive program to tackle some key problems including modeling, processing and statistical estimation of fractional diffusion. Advances made in this program will in turn benefit the developments in related scientific fields.