Renewal Processes of Mittag-Leffler and Wright Type

Mainardi, Francesco; Gorenflo, Rudolf; Vivoli, Alessandro

Fractional Calculus and Applied Analysis (2005)

  • Volume: 8, Issue: 1, page 07-38
  • ISSN: 1311-0454

Abstract

top
2000 MSC: 26A33, 33E12, 33E20, 44A10, 44A35, 60G50, 60J05, 60K05.After sketching the basic principles of renewal theory we discuss the classical Poisson process and offer two other processes, namely the renewal process of Mittag-Leffler type and the renewal process of Wright type, so named by us because special functions of Mittag-Leffler and of Wright type appear in the definition of the relevant waiting times. We compare these three processes with each other, furthermore consider corresponding renewal processes with reward and numerically their long-time behaviour.

How to cite

top

Mainardi, Francesco, Gorenflo, Rudolf, and Vivoli, Alessandro. "Renewal Processes of Mittag-Leffler and Wright Type." Fractional Calculus and Applied Analysis 8.1 (2005): 07-38. <http://eudml.org/doc/11267>.

@article{Mainardi2005,
abstract = {2000 MSC: 26A33, 33E12, 33E20, 44A10, 44A35, 60G50, 60J05, 60K05.After sketching the basic principles of renewal theory we discuss the classical Poisson process and offer two other processes, namely the renewal process of Mittag-Leffler type and the renewal process of Wright type, so named by us because special functions of Mittag-Leffler and of Wright type appear in the definition of the relevant waiting times. We compare these three processes with each other, furthermore consider corresponding renewal processes with reward and numerically their long-time behaviour.},
author = {Mainardi, Francesco, Gorenflo, Rudolf, Vivoli, Alessandro},
journal = {Fractional Calculus and Applied Analysis},
keywords = {26A33; 33E12; 33E20; 44A10; 44A35; 60G50; 60J05; 60K05},
language = {eng},
number = {1},
pages = {07-38},
publisher = {Institute of Mathematics and Informatics Bulgarian Academy of Sciences},
title = {Renewal Processes of Mittag-Leffler and Wright Type},
url = {http://eudml.org/doc/11267},
volume = {8},
year = {2005},
}

TY - JOUR
AU - Mainardi, Francesco
AU - Gorenflo, Rudolf
AU - Vivoli, Alessandro
TI - Renewal Processes of Mittag-Leffler and Wright Type
JO - Fractional Calculus and Applied Analysis
PY - 2005
PB - Institute of Mathematics and Informatics Bulgarian Academy of Sciences
VL - 8
IS - 1
SP - 07
EP - 38
AB - 2000 MSC: 26A33, 33E12, 33E20, 44A10, 44A35, 60G50, 60J05, 60K05.After sketching the basic principles of renewal theory we discuss the classical Poisson process and offer two other processes, namely the renewal process of Mittag-Leffler type and the renewal process of Wright type, so named by us because special functions of Mittag-Leffler and of Wright type appear in the definition of the relevant waiting times. We compare these three processes with each other, furthermore consider corresponding renewal processes with reward and numerically their long-time behaviour.
LA - eng
KW - 26A33; 33E12; 33E20; 44A10; 44A35; 60G50; 60J05; 60K05
UR - http://eudml.org/doc/11267
ER -

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.