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Abstract  

The discrete-time phase type (PH) distributions are used in the numerical solution of many problems. The representation of a PH distribution consists of a vector and a substochastic matrix. The common feature of the PH distributions is that they have rational moment generating function. The moment generating function depends on the eigendecomposition of the transition probability matrix of the PH distribution, but the eigenvalues and eigenvectors are important in other cases as well. Due to the finite precision of the numerical calculations or other reasons, a representation may contain errors that change the eigendecomposition. This paper presents upper bounds on the change of the eigendecomposition when the PH representation is perturbed. Since these bounds do not depend on a particular representation, but they hold for all, the analysed PH representations have uniformly stable spectral decompositions.

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