Related papers: Time-changed generalized fractional Skellam proces…
We study two schemes for a time-fractional Fokker-Planck equation with space- and time-dependent forcing in one space dimension. The first scheme is continuous in time and is discretized in space using a piecewise-linear Galerkin finite…
In this paper, we investigate the solutions for a generalized fractional diffusion equation that extends some known diffusion equations by taking a spatial time-dependent diffusion coefficient and an external force into account, which…
We consider the problem of learning time-varying functions in a distributed fashion, where agents collect local information to collaboratively achieve a shared estimate. This task is particularly relevant in control applications, whenever…
The aim of this paper is the analysis of the fractional Poisson process where the state probabilities $p_k^{\nu_k}(t)$, $t\ge 0$, are governed by time-fractional equations of order $0<\nu_k\leq 1$ depending on the number $k$ of events…
We consider a class of piecewise-deterministic Markov processes where the state evolves according to a linear dynamical system. This continuous time evolution is interspersed by discrete events that occur at random times and change (reset)…
The term \emph{moderate deviations} is often used in the literature to mean a class of large deviation principles that, in some sense, fills the gap between a convergence in probability to zero (governed by a large deviation principle) and…
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…
We use the two-time scale subordination in order to describe dynamical processes in continuous media with a long-term memory. Our consideration touches two physical examples in detail. First we study a temporal evolution of the species…
In this paper, we construct operator fractional L\'evy motion (ofLm), a broad class of non-Gaussian stochastic processes that are covariance operator self-similar, have wide-sense stationary increments and display infinitely divisible…
We consider a continuous-time random walk which is the generalization, by means of the introduction of waiting periods on sites, of the one-dimensional nonhomogeneous random walk with a position-dependent drift known in the mathematical…
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…
In this paper we present the concept of description of random processes in complex systems with the discrete time. It involves the description of kinetics of discrete processes by means of the chain of finite-difference non-Markov equations…
In this paper we investigate the solution of generalized distributed order diffusion equations with composite time fractional derivative by using the Fourier-Laplace transform method. We represent solutions in terms of infinite series in…
Scattering moments provide nonparametric models of random processes with stationary increments. They are expected values of random variables computed with a nonexpansive operator, obtained by iteratively applying wavelet transforms and…
In this paper we study the class of mixed-index time fractional differential equations in which different components of the problem have different time fractional derivatives on the left hand side. We prove a theorem on the solution of the…
In this paper, we study the existence and uniqueness of solutions for general fractional-time parabolic equations of mixture type, and their probabilistic representations in terms of the corresponding inverse subordinators with or without…
From a continuous-time long memory stochastic process, a discrete-time randomly sampled one is drawn. We investigate the second-order properties of this process and establish some time-and frequency-domain asymptotic results. We mainly…
For a spectrally negative L\'evy process, scale functions appear in the solution of two-sided exit problems, and in particular in relation with the Laplace transform of the first time it exits a closed interval. In this paper, we consider…
Using the concept of self-decomposable subordinators introduced in Gardini et al. [11], we build a new bivariate Normal Inverse Gaussian process that can capture stochastic delays. In addition, we also develop a novel path simulation scheme…
In this paper, we consider the time change of the diffusion process on the 2-dimensional unit sphere generated by the Laplace-Beltrami operator, perturbed by means of a longitudinal vector field. First, this is done by addressing the…