On discrete-time semi-Markov processes

Angelica Pachon; Federico Polito; Costantino Ricciuti

doi:10.3934/dcdsb.2020170

On discrete-time semi-Markov processes

Angelica Pachon, Federico Polito, Costantino Ricciuti

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Abstract

In the last years, several authors studied a class of continuous-time semi-Markov processes obtained by time-changing Markov processes by hitting times of independent subordinators. Such processes are governed by integro-differential convolution equations of generalized fractional type. The aim of this paper is to develop a discrete-time counterpart of such a theory and to show relationships and differences with respect to the continuous time case. We present a class of discrete-time semi-Markov chains which can be constructed as time-changed Markov chains and we obtain the related governing convolution type equations. Such processes converge weakly to those in continuous time under suitable scaling limits.

Mathematics Subject Classification: 60K15, 60J10, 60G50, 60G51.

Original language	English
Pages (from-to)	1499-1529
Number of pages	31
Journal	Discrete and Continuous Dynamical Systems B
Volume	26
Issue number	3
DOIs	https://doi.org/10.3934/dcdsb.2020170
Publication status	Published - 1 Aug 2020

Keywords

Semi-Markov processes
discrete-time chains
discrete fractional operators
time change
fractional Bernoulli process
sibuya counting process

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10.3934/dcdsb.2020170Licence: CC BY

1531-3492_2017_11_631 (4)Final published version, 434 KBLicence: CC BY

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title = "On discrete-time semi-Markov processes",

abstract = "In the last years, several authors studied a class of continuous-time semi-Markov processes obtained by time-changing Markov processes by hitting times of independent subordinators. Such processes are governed by integro-differential convolution equations of generalized fractional type. The aim of this paper is to develop a discrete-time counterpart of such a theory and to show relationships and differences with respect to the continuous time case. We present a class of discrete-time semi-Markov chains which can be constructed as time-changed Markov chains and we obtain the related governing convolution type equations. Such processes converge weakly to those in continuous time under suitable scaling limits.Mathematics Subject Classification: 60K15, 60J10, 60G50, 60G51.",

keywords = "Semi-Markov processes, discrete-time chains, discrete fractional operators, time change, fractional Bernoulli process, sibuya counting process",

author = "Angelica Pachon and Federico Polito and Costantino Ricciuti",

note = "Funding Information: A. Pachon has been partially supported by the project “Complex Networks and Data Science” (CES RIS 2019, University of South Wales). Funding Information: Acknowledgments. F. Polito and C. Ricciuti have been partially supported by the project “Memory in Evolving Graphs” (Compagnia di San Paolo-Universit{\`a} di Torino). F. Polito has been also partially supported by INdAM/GNAMPA. Publisher Copyright: {\textcopyright} 2021 American Institute of Mathematical Sciences. All rights reserved. Copyright: Copyright 2021 Elsevier B.V., All rights reserved.",

year = "2020",

month = aug,

day = "1",

doi = "10.3934/dcdsb.2020170",

language = "English",

volume = "26",

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journal = "Discrete and Continuous Dynamical Systems B",

issn = "1553-524x",

publisher = "Southwest Missouri State University",

number = "3",

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T1 - On discrete-time semi-Markov processes

AU - Pachon, Angelica

AU - Polito, Federico

AU - Ricciuti, Costantino

N1 - Funding Information: A. Pachon has been partially supported by the project “Complex Networks and Data Science” (CES RIS 2019, University of South Wales). Funding Information: Acknowledgments. F. Polito and C. Ricciuti have been partially supported by the project “Memory in Evolving Graphs” (Compagnia di San Paolo-Università di Torino). F. Polito has been also partially supported by INdAM/GNAMPA. Publisher Copyright: © 2021 American Institute of Mathematical Sciences. All rights reserved. Copyright: Copyright 2021 Elsevier B.V., All rights reserved.

PY - 2020/8/1

Y1 - 2020/8/1

N2 - In the last years, several authors studied a class of continuous-time semi-Markov processes obtained by time-changing Markov processes by hitting times of independent subordinators. Such processes are governed by integro-differential convolution equations of generalized fractional type. The aim of this paper is to develop a discrete-time counterpart of such a theory and to show relationships and differences with respect to the continuous time case. We present a class of discrete-time semi-Markov chains which can be constructed as time-changed Markov chains and we obtain the related governing convolution type equations. Such processes converge weakly to those in continuous time under suitable scaling limits.Mathematics Subject Classification: 60K15, 60J10, 60G50, 60G51.

AB - In the last years, several authors studied a class of continuous-time semi-Markov processes obtained by time-changing Markov processes by hitting times of independent subordinators. Such processes are governed by integro-differential convolution equations of generalized fractional type. The aim of this paper is to develop a discrete-time counterpart of such a theory and to show relationships and differences with respect to the continuous time case. We present a class of discrete-time semi-Markov chains which can be constructed as time-changed Markov chains and we obtain the related governing convolution type equations. Such processes converge weakly to those in continuous time under suitable scaling limits.Mathematics Subject Classification: 60K15, 60J10, 60G50, 60G51.

KW - Semi-Markov processes

KW - discrete-time chains

KW - discrete fractional operators

KW - time change

KW - fractional Bernoulli process

KW - sibuya counting process

U2 - 10.3934/dcdsb.2020170

DO - 10.3934/dcdsb.2020170

M3 - Article

SN - 1553-524x

VL - 26

SP - 1499

EP - 1529

JO - Discrete and Continuous Dynamical Systems B

JF - Discrete and Continuous Dynamical Systems B

IS - 3

ER -

On discrete-time semi-Markov processes

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