This paper takes under consideration subordinators and their inverse processes (hitting-
times). The governing equations of such processes are presented by means of convolution …

Time-changed Lévy processes include the fractional Poisson process, and the scaling limit
of a continuous time random walk. They are obtained by replacing the deterministic time …

We focus on eventually non-linear abstract Cauchy problems with a generalized fractional
derivative in time. First we prove a local existence and uniqueness result, then we focus on a …

The recent literature on high frequency financial data includes models that use the
difference of two Poisson processes, and incorporate a Skellam distribution for forward …

We present new properties for the Fractional Poisson process (FPP) and the Fractional
Poisson field on the plane. A martingale characterization for FPPs is given. We extend this …

The space-fractional Poisson process is a time-changed homogeneous Poisson process
where the time change is an independent stable subordinator. In this paper, a further …

In this article, convolution-type fractional derivatives generated by Dickman subordinator
and inverse Dickman subordinator are discussed. The Dickman subordinator and its inverse …

The Poisson process suitably models the time of successive events and thus has numerous
applications in statistics, in economics, it is also fundamental in queueing theory. Economic …

Let D (s), s≥ 0 be a non-decreasing Lévy process. The first-hitting time process E (t), t≥ 0
(which is sometimes referred to as an inverse subordinator) defined by E(t)=\inf{s:D(s)>t\} is …

We introduce a fractional generalization of the Erlang Queues M∕ E k∕ 1. Such process is
obtained through a time-change via inverse stable subordinator of the classical queue …