# Accession Number:

## AD0256670

# Title:

## ASYMPTOTIC MULTIVARIATE OCCUPATION TIME DISTRIBUTIONS FOR SEMI-MARKOV PROCESSES

# Descriptive Note:

# Corporate Author:

## STANFORD UNIV CALIF APPLIED MATHEMATICS AND STATISTICS LABS

# Personal Author(s):

# Report Date:

## 1961-05-15

# Pagination or Media Count:

## 1.0

# Abstract:

Asymptotic bivariate normality is established for the cumulative occupation times of two states in a semi-Markov process with countable state space and also for the cumulative sums of functions defined n the occupation times. The asymptotic moments are given exp icitly for a general semiMarkov process with three possible states and a semi-Markov process with countable state space in which F sub ij equals F sub i, i.e., F sub ij independent of j. These results are applied to the zero and one states in a simple MM1 queue. A UTHORAD - 2 AD-256 671Div. 15, 8U 26 M AY OTS price 3.60Applied Mathematics and S TATISTICS Labs., tanford U., Calif. SPECTRAL ANALYSIS OF ASYMPTOTICALLY STATIONARY TIME SERIES, by Emanuel Parzen. 2 May 61, 32p. Technical rept. no. 38 Contract Nonr-22521, Proj. NR-042-993 Unclassified report DESCRIPTORS Spectrographic analysis, Cor relation techniques, Statistical analysis, Communications theory, Mathematics, eries. The conditions under which it can be said that a time series possesses a spectrum are examined. It is shown how to construct a theory of the existe ce, interpretation, and estimation of the spectrum which is more in accord with the manner in which physical scientists use these ideas than the widely accepted definition of the spectrum based on the notion of a stationary process. Conditions for a time series to possess a generalized harmonic analysis are determined. Author