A NOTE ON MATRIX RENEWAL FUNCTION.
Abstract
The Laplace-Steiltjes Transform of the matrix renewal function M(t) 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)
Document Details
- Document Type
- Technical Report
- Publication Date
- Jan 23, 1970
- Accession Number
- AD0701687
Entities
People
- A. M. Kshirsager
- Y. P. Gupta
Organizations
- Southern Methodist University