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# Accession Number:

## AD0737230

# Title:

## A Note on a O-1 Law for Stationary Gaussian Processes,

# Descriptive Note:

# Corporate Author:

## NORTH CAROLINA UNIV CHAPEL HILL DEPT OF STATISTICS

# Report Date:

## 1972-01-01

# Pagination or Media Count:

##
11.0

# Abstract:

## It is shown that a stationary Gaussian process Xt, defined on t 1,2, attains values which exceed any given non-decreasing function ft infinitely often with probability zero or one. The only assumption made is that the covariance function rt go to zero as t goes to infinity. When rt is of smaller order than t sup gamma for some gamma 0, a test is given which distinguishes between the two cases of probability zero and one. Similar results are indicated when, instead, the index t assumes all the values in the interval 0, infinity and the sample paths of xt are continuous. Author

# Distribution Statement:

## APPROVED FOR PUBLIC RELEASE

#