Fractional non-homogeneous Poisson and Pólya-Aeppli processes of order $k$ and beyond

Abstract

We introduce two non-homogeneous processes: a fractional non-homogeneous Poisson process of order $k$ and and a fractional non-homogeneous Pólya-Aeppli process of order $k$. We characterize these processes by deriving their non-local governing equations. We further study the covariance structure of the processes and investigate the long-range dependence property.

35 pages, double spacing, correction of v3

References in corpus (1)

• On Densities of the Product, Quotient and Power of Independent Subordinators

Cited by in corpus (1)

• Generalized Fractional Counting Process