## Technical Report, Issue 78 |

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A+B)x academic analytic function applications assume assumption bilateral boundary point chosen closure COLLEGE OF ENGINEERING components consider convergence CORNELL UNIVERSITY ITHACA corresponding defined Definition degenerate Denoting DEPARTMENT OF OPERATIONS derivatives determinant differentiable discuss domain encompass ENGINEERING CORNELL UNIVERSITY entries equal to zero exist explicitly occur follows Frobenius eigenvalue Furthermore hence hold implies indices i,j inequality inside integrals irreducible nonnegative matrices jointly k-variate probability distribution k-variate semi-Markov matrix Laplace-Stieltjes transform Lemma Marcel F marginal distribution MATRICES by Marcel mean Miller Moreover MULTIVARIATE SEMI-MARKOV MATRICES Neuts nondegeneracy Nondegenerate k-variate semi-Markov nonnegative vectors nonnegative vectors x normalization OPERATIONS RESEARCH pair i,j partly supported Perron Perron-Frobenius eigenvalue positive orthant Probability theory Proof Let properties Purdue University quantities refer Remark respect semi-Markov matrix Q(x sequence smallest real number statement stochastic strictly convex function suitably continuous theorem unilateral unique univariate University and Cornell variables equal YORK