ON THE SPH-DISTRIBUTION CLASS

Following up Neuts‘ idea, the SPH-distribution class associated with bounded Q matrices for infinite Markov chains is defined. The main result in this paper is to characterize the SPH class through the derivatives of the distribution functions. Based on the characterization theorem, closure properties, the expansion, uniform approximation,and the matrix representations of the SPH class are also discussed by the derivatives of the distribution functions at origin.Key words Phase type distribution, absorbing Markov chain, operator theory, SPH- distribution, properties