Asymptotic Properties of Gaussian Processes.
Abstract
The authors consider two problems for separable mean zero Gaussian processes X(t) with correlation functions rho(t,s) for which 1-rho(t,s) is asymptotic to a regularly varying (at zero) function of /t-s/ with exponent 0=or < alpha =or <2. In showing the existence of such (stationary) processes for 0 = or < alpha < 2, the authors relate the magnitude of the tails of the spectral distributionsto the behavior of the covariance function at the origin. For 0 < alpha = or < 2, the authors obtain the asymptotic distribution of the maximum of X(t). This second result is used to obtain a result for X(t) as t approaches infinity similar to the 'so called' law of the iterated logarithm. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Feb 01, 1971
- Accession Number
- AD0721118
Entities
People
- Clifford Qualls
- Hisao Watanabe
Organizations
- University of North Carolina at Chapel Hill