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

Mogens Bladt, Azucena Campillo Navarro, Bo Friis Nielsen

Research output: Contribution to journalJournal articleResearchpeer-review

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 article we provide a number of examples of how to execute the formal arguments.
Original languageEnglish
JournalStochastic Models
Volume32
Issue number1
Pages (from-to)1-19
ISSN1532-6349
DOIs
Publication statusPublished - 2016

Keywords

  • Complex analysis
  • Functional calculus
  • Matrix-exponential
  • Mellin transform
  • Phase-type distributions

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