Statistical estimation and approximation of anomalous diffusion

异常扩散的统计估计和近似

• 批准号: DP0345577
• 负责人: Prof Vo Anh
• 金额: $ 13.61万
• 依托单位: Queensland University of Technology
• 依托单位国家: 澳大利亚
• 项目类别: Discovery Projects
• 财政年份: 2003
• 资助国家: 澳大利亚
• 起止时间: 2003-01-15 至 2007-03-02
• 项目状态: 已结题
• 来源: https://dataportal.arc.gov.au/RGS/Web/Grants/DP0345577
• 关键词: Statistical; estimation; approximation; anomalous; diffusion

This project investigates diffusion processes with long memory, heavy-tailed distributions and higher-order information. Each of these characteristics has been a subject of extensive current research. These processes arise in important applications with significant social/economic benefits such as heat conduction and fluid flow in porous media, propagation of seismic waves, transport of drug molecules in living tissues. Built on our recent fundamental developments of fractional generalised random fields and fractional diffusion equations, this project tackles the key problems of statistical estimation, approximation and prediction of diffusion processes with all the above characteristics in a unified framework not provided by other approaches.

本课题研究具有长记忆、重尾分布和高阶信息的扩散过程。这些特征中的每一个都是当前广泛研究的主题。这些过程出现在具有显著社会/经济效益的重要应用中，例如多孔介质中的热传导和流体流动，地震波的传播，活组织中药物分子的运输。基于我们最近在分数阶广义随机场和分数阶扩散方程方面的基本进展，本项目在一个统一的框架内解决了具有上述所有特征的扩散过程的统计估计、近似和预测的关键问题，而其他方法没有提供这些问题。