Related papers: Fractional discrete processes: compound and mixed …

Fractional Poisson processes, a rapidly growing area of non-Markovian stochastic processes, are useful in statistics to describe data from counting processes when waiting times are not exponentially distributed. We show that the fractional…

In this paper we present multivariate space-time fractional Poisson processes by considering common random time-changes of a (finite-dimensional) vector of independent classical (non-fractional) Poisson processes. In some cases we also…

In this paper, we define a fractional negative binomial process (FNBP) by replacing the Poisson process by a fractional Poisson process (FPP) in the gamma subordinated form of the negative binomial process. First, it is shown that the…

We introduce two non-homogeneous processes: a fractional non-homogeneous Poisson process of order $k$ and and a fractional non-homogeneous P\'olya-Aeppli process of order $k$. We characterize these processes by deriving their non-local…

We consider two independent Gaussian processes that admit a representation in terms of a stochastic integral of a deterministic kernel with respect to a standard Wiener process. In this paper we construct two families of processes, from a…

We study different fractional extensions of the Poisson process and generalized counting processes by introducing time-change represented by the inverse to the sums of stable and tempered stable subordinators. We state the governing…

We present new properties for the Fractional Poisson process and the Fractional Poisson field on the plane. A martingale characterization for Fractional Poisson processes is given. We extend this result to Fractional Poisson fields,…

The fractional Poisson process is a renewal process with Mittag-Leffler waiting times. Its distributions solve a time-fractional analogue of the Kolmogorov forward equation for a Poisson process. This paper shows that a traditional Poisson…

A multivariate fractional Poisson process was recently defined in Beghin and Macci (2016) by considering a common independent random time change for a finite dimensional vector of independent (non-fractional) Poisson processes; moreover it…

We introduce a non-homogeneous fractional Poisson process by replacing the time variable in the fractional Poisson process of renewal type with an appropriate function of time. We characterize the resulting process by deriving its non-local…

In this paper, we introduce and study fractional versions of three compound Poisson processes, namely, the Bell-Touchard process, the Poisson-logarithmic process and the generalized P\'olya-Aeppli process. It is shown that these processes…

We generate the fractional Poisson process by subordinating the standard Poisson process to the inverse stable subordinator. Our analysis is based on application of the Laplace transform with respect to both arguments of the evolving…

This paper introduces the Generalized Fractional Compound Poisson Process (GFCPP), which claims to be a unified fractional version of the compound Poisson process (CPP) that encompasses existing variations as special cases. We derive its…

The fractional non-homogeneous Poisson process was introduced by a time-change of the non-homogeneous Poisson process with the inverse $\alpha$-stable subordinator. We propose a similar definition for the (non-homogeneous) fractional…

A new fractional non-homogeneous counting process has been introduced and developed using the Kilbas and Saigo three-parameter generalization of the Mittag-Leffler function. The probability distribution function of this process reproduces…

We present some correlated fractional counting processes on a finite time interval. This will be done by considering a slight generalization of the processes in Borges et al. (2012). The main case concerns a class of space-time fractional…

In this article, we derive the state probabilities of different type of space- and time-fractional Poisson processes using z-transform. We work on tempered versions of time-fractional Poisson process and space-fractional Poisson processes.…

We prove large deviation principles for two versions of fractional Poisson processes. Firstly we consider the main version which is a renewal process; we also present large deviation estimates for the ruin probabilities of an insurance…

Approximations of fractional Brownian motion using Poisson processes whose parameter sets have the same dimensions as the approximated processes have been studied in the literature. In this paper, a special approximation to the…

We consider a weighted sum of a series of independent Poisson random variables and show that it results in a new compound Poisson distribution which includes the Poisson distribution and Poisson distribution of order k. An explicit…