Space-fractional versions of the negative binomial and Polya-type processes

L. Beghin, P. Vellaisamy

Published 2014-12-10Version 1

In this paper, we introduce a space fractional negative binomial (SFNB) process by subordinating the space fractional Poisson process to a gamma process. Its one-dimensional distributions are derived in terms of generalized Wright functions and their governing equations are obtained. It is a L\'evy process and the corresponding L\'evy measure is given. Extensions to the case of distributed order SFNB process, where the fractional index follows a two-point distribution, is analyzed in detail. Finally, the connections of the SFNB process to a space fractional Polya-type process is also pointed out.