Accession Number : AD0721118

Title :   Asymptotic Properties of Gaussian Processes.

Descriptive Note : Research rept.,

Corporate Author : NORTH CAROLINA UNIV CHAPEL HILL DEPT OF STATISTICS

Personal Author(s) : Qualls,Clifford ; Watanabe,Hisao

Report Date : FEB 1971

Pagination or Media Count : 30

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)

Descriptors :   (*STATISTICAL PROCESSES, PROBABILITY DENSITY FUNCTIONS), STOCHASTIC PROCESSES, STATISTICAL DISTRIBUTIONS, STATISTICAL FUNCTIONS, THEOREMS

Subject Categories : Statistics and Probability

Distribution Statement : APPROVED FOR PUBLIC RELEASE