On the use of functional calculus for phase-type and related distributions

Mogens Bladt, Azucena Campillo Navarro, Bo Friis Nielsen

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Abstract

The area of phase-type distributions is renowned for its ability to obtain closed form formulas or algorithmically exact solutions to many complex stochastic models. The method of functional calculus will provide an additional tool along these lines for establishing results in terms of functions of matrices. Functional calculus, which is a branch of operator theory frequently associated with complex analysis, can be applied to phase-type and matrix-exponential distributions in a rather straightforward way. In this paper we provide a number of examples on how to execute the formal arguments.
Original languageEnglish
Place of PublicationKgs. Lyngby
PublisherTechnical University of Denmark
Number of pages25
Publication statusPublished - 2014
SeriesDTU Compute-Technical Report-2014
Number18
ISSN1601-2321

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