In:
Operations Research, Institute for Operations Research and the Management Sciences (INFORMS), Vol. 18, No. 6 ( 1970-12), p. 1168-1181
Abstract:
A finite discrete nonstationary Markov chain is completely characterized (after the initial probability distribution has taken effect) by its time sequence of transition probability matrices P i . The ith causative matrix C i is defined as the product P i −1 (if it exists) times P i+1 . Thus, the causative matrices are analogous to derivatives in calculus as an indication of rate of change. The eigenvalues and eigenvectors of a constant causative matrix C have been found useful in their connection with the tendency of the chain to be convergent or divergent. Results for two-state chains are presented in some detail. A comprehensive bibliography of papers on non-stationary chains is included.
Type of Medium:
Online Resource
ISSN:
0030-364X
,
1526-5463
DOI:
10.1287/opre.18.6.1168
Language:
English
Publisher:
Institute for Operations Research and the Management Sciences (INFORMS)
Publication Date:
1970
detail.hit.zdb_id:
2019440-7
detail.hit.zdb_id:
123389-0
SSG:
3,2
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