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

近年来，人们对分形模型的推导越来越感兴趣，以代表某些物理现象，如多孔介质中的扩散和传输，海洋和大气湍流，气候学等。分形调和分析的最新进展和我们自己的分数广义随机场的发展，使我们能够制定一个全面的计划，以解决一些关键问题，包括建模，处理和统计估计的分数扩散。该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.