THE RELATIONSHIP BETWEEN DIMENSION AND FRACTAL INDEX FOR STATIONARY STOCHASTIC PROCESSES
成果类型：
Article
署名作者：
Hall, Peter; Roy, Rahul
署名单位：
Australian National University; Indian Statistical Institute; Indian Statistical Institute Delhi
刊物名称：
ANNALS OF APPLIED PROBABILITY
ISSN/ISSBN：
1050-5164
DOI：
10.1214/aoap/1177005210
发表日期：
1994
页码：
241-253
关键词：
摘要：
For Gaussian processes there is a simple and well-known relationship between the fractal dimension of sample paths and the fractal index of the covariance function. This property is of considerable practical interest, since it forms the basis of several estimators of fractal dimension. Motivated by statistical applications involving non-Gaussian processes, we discuss the relationship in a wider context. We show that the relationship fails in some circumstances, but nevertheless does hold in a variety of cases.