MVME coincides with MME* via realization theorem and augmentations; MPH* is strictly contained in MVPH from the trivariate case, separated by a new factorization condition with a Wishart trace distribution as counterexample.
Rap-modulated fluid processes: First passages and the stationary distribution.Stochastic Processes and their Ap- plications, 149:308–340
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Equivalence and Separation for Multivariate Matrix-Exponential and Phase-Type Distribution Classes
MVME coincides with MME* via realization theorem and augmentations; MPH* is strictly contained in MVPH from the trivariate case, separated by a new factorization condition with a Wishart trace distribution as counterexample.