Related papers: Some recent advances in theory and simulation of f…
The diffusion of a particle in a crowded environment typically proceeds through three regimes: for very short times the particle diffuses freely until it collides with an obstacle for the first time, while for very long times diffusion the…
In the present paper, we characterize the behavior of supercritical branching processes in random environment with linear fractional offspring distributions, conditioned on having small, but positive values at some large generation. As it…
We propose threshold diffusion processes as unique solutions to stochastic differential equations with step-function coefficients, and obtain explicit expressions for the conditional Laplace transform of the hitting times and the potential…
Recently, fractional derivatives have been employed to analyze various systems in engineering, physics, finance and hidrology. For instance, they have been used to investigate anomalous diffusion processes which are present in different…
Using a microfluidics device filled with a colloidal suspension of microspheres, we test the laws of diffusion in the limit of small particle numbers. Our focus is not just on average properties such as the mean flux, but rather on the…
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…
The change of the effective dimension of spacetime with the probed scale is a universal phenomenon shared by independent models of quantum gravity. Using tools of probability theory and multifractal geometry, we show how dimensional flow is…
We construct a flow of continuous time and discrete state branching processes. Some scaling limit theorems for the flow are proved, which lead to the path-valued branching processes and nonlocal branching superprocesses over the positive…
We consider a simple mean reverting diffusion process, with piecewise constant drift and diffusion coefficients, discontinuous at a fixed threshold. We discuss estimation of drift and diffusion parameters from discrete observations of the…
Zolotarev proved a duality result that relates stable densities with different indices. In this paper, we show how Zolotarev duality leads to some interesting results on fractional diffusion. Fractional diffusion equations employ fractional…
We study the distribution of first passage time (FPT) in Levy type of anomalous diffusion. Using recently formulated fractional Fokker-Planck equation we obtain three results. (1) We derive an explicit expression for the FPT distribution in…
We study invariant solutions of a certain class of time-fractional diffusion-wave equations with variable coefficients via Lie symmetry analysis. In physics, the fractional diffusion equation describes transport dynamics that are governed…
It is a well known fact that subdiffusion equations in terms of fractional derivatives can be obtained from Continuous Time Random Walk (CTRW) models with long-tailed waiting time distributions. Over the last years various authors have…
We consider a basic one-dimensional model of diffusion which allows to obtain a diversity of diffusive regimes whose speed depends on the moments of the per-site trapping time. This model is closely related to the continuous time random…
The main purpose of this note is to point out the relevance of the Mittag-Leffler probability distribution in the so-called thinning theory for a renewal process with a queue of power law type. This theory, formerly considered by Gnedenko…
The fractional Poisson process has recently attracted experts from several fields of study. Its natural generalization of the ordinary Poisson process made the model more appealing for real-world applications. In this paper, we generalized…
We investigate the diffusive motion of an overdamped classical particle in a 1D random potential using the mean first-passage time formalism and demonstrate the efficiency of this method in the investigation of the large-time dynamics of…
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 derive some additional results on the Bienyam\'e-Galton-Watson branching process with $\theta -$linear fractional branching mechanism, as studied in \cite{Sag}. This includes: the explicit expression of the limit laws in both the…
We consider the distribution of the duration time, the time elapsed since it began, of a diffusion process given its present position, under the assumption that the process began at the origin. For unbiased diffusion, the distribution does…