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

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On the use of functional calculus for phase-type and related distributions. / Bladt, Mogens; Navarro, Azucena Campillo; Nielsen, Bo Friis.

In: Stochastic Models, Vol. 32, No. 1, 2016, p. 1-19.

Research output: Contribution to journalJournal article – Annual report year: 2015Researchpeer-review

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@article{fd39a343a13a4e3586e15ec8be3da910,
title = "On the use of functional calculus for phase-type and related distributions",
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.",
keywords = "Complex analysis, Functional calculus, Matrix-exponential, Mellin transform, Phase-type distributions",
author = "Mogens Bladt and Navarro, {Azucena Campillo} and Nielsen, {Bo Friis}",
year = "2016",
doi = "10.1080/15326349.2015.1064773",
language = "English",
volume = "32",
pages = "1--19",
journal = "Stochastic Models",
issn = "1532-6349",
publisher = "Taylor & Francis Inc",
number = "1",

}

RIS

TY - JOUR

T1 - On the use of functional calculus for phase-type and related distributions

AU - Bladt, Mogens

AU - Navarro, Azucena Campillo

AU - Nielsen, Bo Friis

PY - 2016

Y1 - 2016

N2 - 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.

AB - 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.

KW - Complex analysis

KW - Functional calculus

KW - Matrix-exponential

KW - Mellin transform

KW - Phase-type distributions

U2 - 10.1080/15326349.2015.1064773

DO - 10.1080/15326349.2015.1064773

M3 - Journal article

VL - 32

SP - 1

EP - 19

JO - Stochastic Models

JF - Stochastic Models

SN - 1532-6349

IS - 1

ER -