TY - JOUR
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 -