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# Accession Number:

## AD0701687

# Title:

## A NOTE ON MATRIX RENEWAL FUNCTION.

# Descriptive Note:

## Technical rept.,

# Corporate Author:

## SOUTHERN METHODIST UNIV DALLAS TEX DEPT OF STATISTICS

# Report Date:

## 1970-01-23

# Pagination or Media Count:

##
12.0

# Abstract:

## The Laplace-Steiltjes Transform of the matrix renewal function Mt of a Markov Renewal process is expanded in powers of the argument s, in this paper, by using a generalized inverse of the matrix I-P sub 0, where P sub 0 is the transition probability matrix of the imbedded Markov chain. This helps in obtaining the values of moments of any order of the number of renewals and also of the moments of the first passage times, for large values of t, the time. All the results of renewal theory are hidden under the Laplacian curtain and this expansion helps to lift this curtain at least for large values of t and is thus useful in applications of Markov Renewal processes to inventory control of repairable items, and to counter theory. Author

# Distribution Statement:

## APPROVED FOR PUBLIC RELEASE

#