Space-Fractional Versions of the Negative Binomial and Polya-Type Processes

L. Beghin () and P. Vellaisamy ()
Additional contact information
L. Beghin: Sapienza University of Rome
P. Vellaisamy: Indian Institute of Technology Bombay

Methodology and Computing in Applied Probability, 2018, vol. 20, issue 2, 463-485

Abstract: Abstract In this paper, we introduce a space fractional negative binomial process (SFNB) by time-changing the space fractional Poisson process by a gamma subordinator. Its one-dimensional distributions are derived in terms of generalized Wright functions and their governing equations are obtained. It is a Lévy process and the corresponding Lévy measure is given. Extensions to the case of distributed order SFNB, where the fractional index follows a two-point distribution, are investigated in detail. The relationship with space fractional Polya-type processes is also discussed. Moreover, we define and study multivariate versions, which we obtain by time-changing a d-dimensional space-fractional Poisson process by a common independent gamma subordinator. Some applications to population’s growth and epidemiology models are explored. Finally, we discuss algorithms for the simulation of the SFNB process.

Keywords: Fractional negative binomial process; Stable subordinator; Wright function; Polya-type process; Governing equations; Primary: 60G22; Secondary: 60G51; 60E05 (search for similar items in EconPapers)
Date: 2018
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3)

Downloads: (external link)
http://link.springer.com/10.1007/s11009-017-9561-8 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:metcap:v:20:y:2018:i:2:d:10.1007_s11009-017-9561-8

Ordering information: This journal article can be ordered from
https://www.springer.com/journal/11009

DOI: 10.1007/s11009-017-9561-8

Access Statistics for this article

Methodology and Computing in Applied Probability is currently edited by Joseph Glaz

More articles in Methodology and Computing in Applied Probability from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().