A Markovian canonical form of second-order matrix-exponential processes (Q2427191)

The paper considers second-order matrix-exponential processes. It is organized as follows. Introduction is given in Section 1. Section 2 introduces the distribution, which have a second-order rational Laplace transform, along with their matrix representations. After a discussion, the known equivalences ME(2) \( \equiv \)PH(2) \( \equiv \)APH(2) will become obvious. In Section 3, it outlines the different definitions of the stochastic processes MEP(2)s, MAP(2)s and AMAP(2)s. Section 4 introduces the general canonical form for second-order arrival processes. Its correlation bounds are first derived in the context of restricted AMAP(2)s and then shown in Section 5 to extend to MEP(2)s. This proves the equivalence MEP(2) \( \equiv \)(A)MAP(2). Section 6 outlines how the theoretical results of this paper can be applied in practice and provides a fitting procedure for the general canonical form. Finally, Section 7 summarizes and concludes this paper.