We consider two fractional versions of a family of nonnegative integer-valued processes. We
prove that their probability mass functions solve fractional Kolmogorov forward equations …

The first-exit time process of an inverse Gaussian Lévy process is considered. The one-
dimensional distribution functions of the process are obtained. They are not infinitely …

We derive the governing equation of the Tempered Stable Subordinator (hereafter TSS),
which generalizes the space-fractional differential equation satisfied by the law of the α …

In this paper we study the fractional Brownian motion (FBM) time changed by the inverse
Gaussian (IG) process and its inverse, called the inverse to the inverse Gaussian (IIG) …

In this study, a multivariate ARMA–GARCH model with fractional generalized hyperbolic
innovations exhibiting fat-tail, volatility clustering, and long-range dependence properties is …

A fractional normal inverse Gaussian (FNIG) process is a fractional Brownian motion
subordinated to an inverse Gaussian process. This paper shows how the FNIG process …

Working on product lifetime data is of significant importance for evaluating safety and
reliability, predicting remaining useful life and formulating maintenance strategy or …

We introduce the class of higher order fractional stable motions that can exhibit
hyperdiffusive spreading with heavy tails. We define the class as a generalization of higher …

In this paper, a new stochastic process called generalized fractional Laplace motion (GFLM)
is introduced. This process is obtained by superposition of n th-order fractional Brownian …

In this paper, we introduce a six parameter generalized extended inverse Gaussian density
function involving a confluent hypergeometric function of two variables Ψ2. We derive some …