多指标随机过程样本轨道的分形特征及其应用

、Hausdorff Abstract: The purpose of the project is to show further the fractal.characters of sample paths of multi-parameter stochastic processes and to investigate the singular structures of random measures associated with the.stochastic processes. The Hausdorff measure for the level sets of multi-parameter symmetric stable processes has been obtained and the inner.connection of the measures and local times for it has been demonstrated, which describes the fractal nature for the level sets of this kind of processes.As we know, it is always one of the focuses in the field of random fractal. The reasult of the existence and continuity of the local time for multi-parameter stochastic processes with stable components has been got in the project. Then we gained the measure for the random fractal sets such as the range and graph of this kind of processes. Furthermore, a progress besides the mentioned above in the project is that we have resolved the multifractal analysis of the sample paths for Brownian sheet, that is the multifractal decomposition of.white noise in high dimension.

本项目拟深入研究多指标随机过程样本轨道的分形特征。力图解决包括稳定单的水平集和2N=D情况维纳单象集在内的随机分形集的测度问题，它们均是该研究领域中十分重要的前沿问题，本项目还拟研究计算机上实现多指标随机过程（如稳定单）产生的随机分形集（如图集曲面、水平集）对自然景物图象仿真模拟问题，它在多媒体技术应用方面有重要意义。