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一类非高斯平稳过程与随机场的分形维数估计AI 解读

We present the asymptotic distribution theory for a class of increment-based estimators of the fractal dimension of a random field of the form g{X(t)}, where g:R→R is an unknown smooth function and X(t) is a real-valued stationary Gaussian field on Rd, d=1 or 2, whose covariance function obeys a power law at the origin. The relevant theoretical framework here is “fixed domain” (or “infill”) asymptotics. Surprisingly, the limit theory in this non-Gaussian case is somewhat…

基于周期图的分形性质估计量AI 解读

We suggest an estimator, based on the periodogram, of the fractal index and fractal dimension of a continuous, stationary Gaussian process. We argue that the cosine part of the periodogram is more appropriate than the full periodogram for this application. The term "semiperiodogram" is used to describe the cosine component, and our estimator is based on simple linear regression of the logarithm of the semiperiodogram on the algorithm of frequency. Theoretical properties of…