Related papers: Generalized Fractional Counting Process

In this paper, we study a Skellam type variant of the generalized counting process (GCP), namely, the generalized Skellam process. Some of its distributional properties such as the probability mass function, probability generating function,…

In this paper, we define a compound generalized fractional counting process (CGFCP) which is a generalization of the compound versions of several well-known fractional counting processes. We obtain its mean, variance, and the fractional…

Traditionally, fractional counting processes, such as the fractional Poisson process, etc. have been defined using fractional differential and integral operators. Recently, Laskin (2024) introduced a generalized fractional counting process…

We introduce a non-homogeneous version of the generalized counting process (GCP), namely, the non-homogeneous generalized counting process (NGCP). We time-change the NGCP by an independent inverse stable subordinator to obtain its…

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…

In this paper, we study the composition of two independent GCPs which we call the iterated generalized counting process (IGCP). Its distributional properties such as the transition probabilities, probability generating function, state…

A non-Markovian counting process, the `generalized fractional Poisson process' (GFPP) introduced by Cahoy and Polito in 2013 is analyzed. The GFPP contains two index parameters $0<\beta\leq 1$, $\alpha >0$ and a time scale parameter.…

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 introduce and study a multiparameter version of the generalized counting process (GCP), where there is a possibility of finitely many arrivals simultaneously. We call it the multiparameter GCP. In a particular case, it is uniquely…

In this paper, we introduce drifted versions of the generalized counting process (GCP) with a deterministic drift and a random drift. The composition of stable subordinator with an independent inverse stable subordinator is taken as the…

In this paper, we study a multivariate version of the generalized counting process (GCP) and discuss its various time-changed variants. The time is changed using random processes such as the stable subordinator, inverse stable subordinator,…

Recently, a generalized Bernoulli process (GBP) was developed as a stationary binary sequence whose covariance function obeys a power law. In this paper, we further develop generalized Bernoulli processes, reveal their asymptotic behaviors,…

We survey the 'generalized fractional Poisson process' (GFPP). The GFPP is a renewal process generalizing Laskin's fractional Poisson counting process and was first introduced by Cahoy and Polito. The GFPP contains two index parameters with…

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…

This paper introduces the Generalized Space-Time Fractional Skellam Process (GSTFSP) and the Generalized Space Fractional Skellam Process (GSFSP). We investigate their distributional properties including the probability generating function…

In this paper, we study the merging and splitting of generalized counting processes (GCPs). First, we study the merging of a finite number of independent GCPs and then extend it to the case of countably infinite. The merged process is…

This paper introduces the Non-homogeneous Generalized Skellam process (NGSP) and its fractional version NGFSP by time changing it with an independent inverse stable subordinator. We study distributional properties for NGSP and NGFSP…

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…

This paper presents a fractional generalized Cauchy process (FGCP) with an additive and a multiplicative Gaussian white noise for describing subordinated anomalous fluctuations. The FGCP displays intermittent dynamics during random time…

In this paper, we introduce a generalized fractional negative binomial process (GFNBP) by time changing the fractional Poisson process with an independent Mittag-Leffler (ML) Levy subordinator. We study its distributional properties and its…