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Documents authored by Telek, Miklós

Document
DOI: 10.4230/DagSemProc.07461.5
Current results and open questions on PH and MAP characterization

Authors: Levente Bodrog, Armin Heindl, Gábor Horváth, Miklós Telek, and András Horváth

Published in: Dagstuhl Seminar Proceedings, Volume 7461, Numerical Methods for Structured Markov Chains (2008)

Abstract
Stochastic processes with matrix exponential kernels have a wide range of applications due to the availability of efficient matrix analytic methods. The characterization of these processes is in progress in recent years. Basic questions like the flexibility, the degree of freedom, the most efficient (canonical) representation of these models are under study. The presentation collects a set of available results and related open questions.
Cite as

Levente Bodrog, Armin Heindl, Gábor Horváth, Miklós Telek, and András Horváth. Current results and open questions on PH and MAP characterization. In Numerical Methods for Structured Markov Chains. Dagstuhl Seminar Proceedings, Volume 7461, pp. 1-6, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2008)

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@InProceedings{bodrog_et_al:DagSemProc.07461.5,
  author =	{Bodrog, Levente and Heindl, Armin and Horv\'{a}th, G\'{a}bor and Telek, Mikl\'{o}s and Horv\'{a}th, Andr\'{a}s},
  title =	{{Current results and open questions on PH and MAP characterization}},
  booktitle =	{Numerical Methods for Structured Markov Chains},
  pages =	{1--6},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2008},
  volume =	{7461},
  editor =	{Dario Bini and Beatrice Meini and Vaidyanathan Ramaswami and Marie-Ange Remiche and Peter Taylor},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.07461.5},
  URN =		{urn:nbn:de:0030-drops-14010},
  doi =		{10.4230/DagSemProc.07461.5},
  annote =	{Keywords: PH distribution, ME distribution, MAP, MEP}
}
Document
DOI: 10.4230/DagSemProc.07461.12
On the Properties of Moments of Matrix Exponential Distributions and Matrix Exponential Processes

Authors: Levente Bodrog, András Horváth, and Miklós Telek

Published in: Dagstuhl Seminar Proceedings, Volume 7461, Numerical Methods for Structured Markov Chains (2008)

Abstract
In this paper we provide properties of moments of matrix exponential distributions and joint moments of matrix exponential processes. Based on the provided properties, an algorithm is presented to compute any finite dimensional moments of these processes based on a set of required (low order) moments. This algorithm does not require the computation of any representation of the given process. We present some related examples to demonstrate the potential use of the properties of moments.
Cite as

Levente Bodrog, András Horváth, and Miklós Telek. On the Properties of Moments of Matrix Exponential Distributions and Matrix Exponential Processes. In Numerical Methods for Structured Markov Chains. Dagstuhl Seminar Proceedings, Volume 7461, pp. 1-12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2008)

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@InProceedings{bodrog_et_al:DagSemProc.07461.12,
  author =	{Bodrog, Levente and Horv\'{a}th, Andr\'{a}s and Telek, Mikl\'{o}s},
  title =	{{On the Properties of Moments of Matrix Exponential Distributions and Matrix Exponential Processes}},
  booktitle =	{Numerical Methods for Structured Markov Chains},
  pages =	{1--12},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2008},
  volume =	{7461},
  editor =	{Dario Bini and Beatrice Meini and Vaidyanathan Ramaswami and Marie-Ange Remiche and Peter Taylor},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.07461.12},
  URN =		{urn:nbn:de:0030-drops-13943},
  doi =		{10.4230/DagSemProc.07461.12},
  annote =	{Keywords: Matrix exponential process, Markov arrival process, Matrix exponential distribution, phase type distribution}
}
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