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Multivariate semi-markov matrices

Published online by Cambridge University Press:  09 April 2009

Marcel F. Neuts  and
Peter Purdue
Marcel F. Neuts
Affiliation:
Purdue University
Peter Purdue
Affiliation:
Cornell University
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Finite matrices with entries pij Fij (x1,…, xk), where {pij} is stochastic and Fij(.) is a k-variate probability distribution are discussed. It is shown that the matrix of k-variate Laplace-Stieltjes transforms of the Pij Fij(x1, …, xk) has a Perron-Frobenius eigenvalue which is a convex function in k variables in a suitably defined region. The values of the partial derivatives near the origin of this maximal eigenvalue are exhibited. They are quantities of interest in a variety of applications in Probability theory.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 13 , Issue 1 , February 1972 , pp. 107 - 113
Copyright
Copyright © Australian Mathematical Society 1972

References

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