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

Authors :
Beghin, L.
Vellaisamy, P.
Source :
Methodology & Computing in Applied Probability; Jun2018, Vol. 20 Issue 2, p463-485, 23p
Publication Year :
2018

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. [ABSTRACT FROM AUTHOR]

Details

Language :
English
ISSN :
13875841
Volume :
20
Issue :
2
Database :
Complementary Index
Journal :
Methodology & Computing in Applied Probability
Publication Type :
Academic Journal
Accession number :
129685906
Full Text :
https://doi.org/10.1007/s11009-017-9561-8