d维平稳高斯过程的极函数及其相关维数

Polar Functions and Relative Dimension for d-Dimensional Stationary Gaussian Processes

研究了d维平稳高斯过程样本轨道的分形性质,由Testard的方法,得到了其极函数的特征及相关维数.此结果包含并推广了布朗运动的结果,Polya过程为其特例.

Fractal properties of sample path of d-dimensional stationary Gaussian processes are investigated. Properties of polar functions and relative dimension are obtained via Testard's method. This result contains and extends the result of Brownian motion. Polya process is its special case.