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.

On discrete-time semi-Markov processes

Federico Polito;Costantino Ricciuti
2021-01-01

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.
2021
26
3
1499
1529
https://arxiv.org/pdf/1807.07932
Angelica Pachon, Federico Polito, Costantino Ricciuti
File in questo prodotto:
File Dimensione Formato  
published.pdf

Accesso riservato

Descrizione: pdf
Tipo di file: PDF EDITORIALE
Dimensione 451.85 kB
Formato Adobe PDF
451.85 kB Adobe PDF   Visualizza/Apri   Richiedi una copia

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2318/1730666
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 10
  • ???jsp.display-item.citation.isi??? 10
social impact