This paper provides a general framework for establishing the relation
between various moments of matrix exponential and Markovian
processes. Based on this framework we present an algorithm to compute
any finite dimensional moments of these processes based on a set of
required (low order) moments. This algorithm does not require the
computation of any representation of the given process. We present a
series of related results and numerical examples to demonstrate the
potential use of the obtained moment relations.
Keywords: Matrix exponential process, Markov arrival process,
Matrix exponential distribution, phase type distribution.