Related papers: Time-changed generalized fractional Skellam proces…
In this paper, we study a multivariate gamma subordinator whose components are independent gamma processes subject to a random time governed by an independent negative binomial process. We derive the explicit expressions for its joint…
Continuous time random walks are non-Markovian stochastic processes, which are only partly characterized by single-time probability distributions. We derive a closed evolution equation for joint two-point probability density functions of a…
In this paper, we obtain additional results for a fractional counting process introduced and studied by Di Crescenzo et al. (2016). For convenience, we call it the generalized fractional counting process (GFCP). It is shown that the…
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…
We define two new classes of stochastic processes, called tempered fractional L\'{e}vy process of the first and second kinds (TFLP and TFLP $I\!I$, respectively). TFLP and TFLP $I\!I$ make up very broad finite-variance, generally…
In this paper, we consider a type of time-changed Markov process, where the time-change is an inverse killed subordinator. This can be seen as an extension of Chen (Chen, Z., Time fractional equations and probabilistic representation, Chaos…
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…
We study a linear-fractional Bienaym\'e-Galton-Watson process with a general type space. The corresponding tree contour process is described by an alternating random walk with the downward jumps having a geometric distribution. This leads…
In this article, we provide different representations for a time-fractional birth and death process $N_{\alpha}(t)$, whose transition probabilities are governed by a time-fractional system of differential equations. More specifically, we…
We define a new family of multivariate stochastic processes over a finite time horizon that we call Generalised Liouville Processes (GLPs). GLPs are Markov processes constructed by splitting L\'evy random bridges into non-overlapping…
The first passage time process of a L\'evy subordinator with heavy-tailed L\'evy measure has long-range dependent paths. The random fluctuations that appear under two natural schemes of summation and time scaling of such stochastic…
We introduce a stochastic fractional calculus. As an application, we present a stochastic fractional calculus of variations, which generalizes the fractional calculus of variations to stochastic processes. A stochastic fractional…
In this paper, we define a tempered space-time fractional negative binomial process (TSTFNBP) by subordinating the fractional Poisson process with an independent tempered Mittag-Leffler L\'{e}vy subordinator. We study its distributional…
We consider a fractional counting process with jumps of amplitude $1,2,\ldots,k$, with $k\in \mathbb{N}$, whose probabilities satisfy a suitable system of fractional difference-differential equations. We obtain the moment generating…
We define a time-changed fractional Ornstein-Uhlenbeck process by composing a fractional Ornstein-Uhlenbeck process with the inverse of a subordinator. Properties of the moments of such process are investigated and the existence of the…
In this paper we study a new generalization of the kinetic equation emerging in run-and-tumble models. We show that this generalization leads to a wide class of generalized fractional kinetic (GFK) and telegraph-type equations depending by…
Many real time-series exhibit behavior adequate to long range dependent data. Additionally very often these time-series have constant time periods and also have characteristics similar to Gaussian processes although they are not Gaussian.…
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…
We introduce a generalized mixed fractional Brownian motion (gmfBm) as a linear combination of two independent fractional Brownian motions with possibly different Hurst indices and investigate conditions under which the time-changed gmfBm…
In recent years, instanton calculus has successfully been employed to estimate tail probabilities of rare events in various stochastic dynamical systems. Without further corrections, however, these estimates can only capture the exponential…