Related papers: The Mittag-Leffler function in the thinning theory…
Anomalous transport is usually described either by models of continuous time random walks (CTRW) or, otherwise by fractional Fokker-Planck equations (FFPE). The asymptotic relation between properly scaled CTRW and fractional diffusion…
The function $t \mapsto E_{\alpha}(\lambda t^\alpha)$ is widely regarded as the fractional analogue of the exponential function, yet its algebraic properties remain poorly understood. In particular, standard references lack a rigorous proof…
Mittag-Leffler analysis is an infinite dimensional analysis with respect to non-Gaussian measures of Mittag-Leffler type which generalizes the powerful theory of Gaussian analysis and in particular white noise analysis. In this paper we…
Renewal process is a point process where an inter-event time between successive renewals is an independent and identically distributed random variable. Alternating renewal process is a dichotomous process and a slight generalization of the…
We review the function theoretical properties of the Mittag-Leffler function $E_{a,b}\left( z\right) $ in a self-contained manner, but also add new results; more than half is new!
In this paper we study finite velocity planar random motions with an infinite number of possible directions, where the number of changes of direction is randomized by means of an inhomogeneous fractional Poisson distribution. We first…
Weak convergence of maxima of dependent sequences of identically distributed continuous random variables is studied under normalizing sequences arising as subsequences of the normalizing sequences from an associated iid sequence. This…
Frequency-dependent acoustical loss due to a multitude of physical mechanisms is commonly modeled by multiple relaxations. For discrete relaxation distributions, such models correspond with causal wave equations of integer-order temporal…
Citation distributions are crucial for the analysis and modeling of the activity of scientists. We investigated bibliometric data of papers published in journals of the American Physical Society, searching for the type of function which…
The method of potential solutions of Fokker-Planck equations is used to develop a transport equation for the joint probability of N stochastic variables with Lochner's generalized Dirichlet distribution (R.H. Lochner, A Generalized…
We present some product representations for random variables with the Linnik, Mittag-Leffler and Weibull distributions and establish the relationship between the mixing distributions in these representations. The main result is the…
We consider the distribution of the binomial probability mass function (pmf) among arithmetic progressions and obtain an average-type theorem. As applications, we consider the possible visits to a kind of sieved sets of integers or lattice…
Spatial spread of minority carriers produced by optical excitation in semiconductors is usually well described by a diffusion equation. The classical diffusion process can be viewed as a result of a random walk of particles in which every…
The foundations of the fractional diffusion equation are investigated based on coupled and decoupled continuous time random walks (CTRW). For this aim we find an exact solution of the decoupled CTRW, in terms of an infinite sum of stable…
Non-linear renewal theory is extended to include random walks perturbed by both a slowly changing sequence and a stationary one. Main results include a version of the Key Renewal Theorem, a derivation of the limiting distribution of the…
We introduce and study here a renewal process defined by means of a time-fractional relaxation equation with derivative order $\alpha(t)$ varying with time $t\geq0$. In particular, we use the operator introduced by Scarpi in the Seventies…
It is known that backward iterations of independent copies of a contractive random Lipschitz function converge almost surely under mild assumptions. By a sieving (or thinning) procedure based on adding to the functions time and space…
In this study, we establish a significant connection between certain subclasses of complex order univalent functions and the Mittag-Leffler-type Poisson distribution series. We provide criteria for these series to belong to the specific…
We consider the problem of diffusion with stochastic resetting in a population of random walks where the diffusion coefficient is not constant, but behaves as a power-law of the average resetting rate of the population. Resetting occurs…
Functionals of Brownian motion have diverse applications in physics, mathematics, and other fields. The probability density function (PDF) of Brownian functionals satisfies the Feynman-Kac formula, which is a Schrodinger equation in…