Related papers: L\'evy flights on the half line
The {\alpha}-stable L\'evy process, commonly used to describe L\'evy flight, is characterized by discontinuous jumps and is widely used to model anomalous transport phenomena. In this study, we investigate the associated exit problem and…
In a recent paper (Abe S 2013 Phys. Rev. E 88 022142), a variational principle has been formulated for spatiotemporally-fractional Fokker-Planck equations and applied to derivations of their approximate analytic solutions based on the…
Non-Gaussian L\'evy noises are present in many models for understanding underlining principles of physics, finance, biology and more. In this work, we consider the Fokker-Planck equation(FPE) due to one-dimensional asymmetric L\'evy motion,…
In this paper, we develop a numerical method for the L\'evy-Fokker-Planck equation with the fractional diffusive scaling. There are two main challenges. One comes from a two-fold nonlocality, that is, the need to apply the fractional…
The stationary reflected Brownian motion in a three-quarter plane has been rarely analyzed in the probabilistic literature, in comparison with the quarter plane analogue model. In this context, our main result is to prove that the…
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 consider a Levy flyer of order alpha that starts from a point x0 on an interval [O,L] with absorbing boundaries. We find a closed-form expression for the average number of flights the flyer takes and the total length of the flights it…
We use the Fokker Planck equation as a starting point for studying the orientational probability distribution of an Active Brownian Particle (ABP) in $(d+1)$ dimensions. This Fokker Planck equation admits an exact solution in series form…
We consider a forager diffusing via a fractional heat equation and we introduce several efficiency functionals whose optimality is discussed in relation to the L\'evy exponent of the evolution equation. Several biological scenarios, such as…
Fractional Levy motion (fLm) is the natural generalization of fractional Brownian motion in the context of self-similar stochastic processes and stable probability distributions. In this paper we give an explicit derivation of the…
We give a probabilistic numerical method for solving a partial differential equation with fractional diffusion and nonlinear drift. The probabilistic interpretation of this equation uses a system of particles driven by L\'evy alpha-stable…
By using the backward fractional Fokker-Planck equation we investigate the barrier crossing event in the presence of Levy noise. After shortly review recent results obtained with different approaches on the time characteristics of the…
We study the distribution of occupation times for a one-dimensional random walk restricted to a finite interval by reflecting boundary conditions. At short times the classical bimodal distribution due to L\'evy is reproduced with walkers…
This paper investigates the probability distribution of solutions to McKean--Vlasov stochastic differential equations driven by fractional Brownian motion with Hurst parameter H>1/2. Our main contribution is the derivation of the associated…
We consider different generalizations of the Fokker-Planck-equation devised to describe Levy processes in potential force fields. We show that such generalizations can proceed along different lines. On one hand, Levy statistics can emerge…
We study the first passage time (FPT) problem in Levy type of anomalous diffusion. Using the recently formulated fractional Fokker-Planck equation, we obtain an analytic expression for the FPT distribution which, in the large passage time…
We introduce a fractional Fokker-Planck equation (FFPE) for Levy flights in the presence of an external field. The equation is derived within the framework of the subordination of random processes which leads to Levy flights. It is shown…
A wide class of non-stationary superdiffusive transport on a uniform background with a power-law decay, at large distances, of the step-length probability distribution function (PDF) is shown to possess an automodel solution. The solution…
The Airy distribution function describes the probability distribution of the area under a Brownian excursion over a unit interval. Surprisingly, this function has appeared in a number of seemingly unrelated problems, mostly in computer…
We solve the time-dependent Fokker-Planck equation for a two-dimensional active Brownian particle exploring a rectangular domain with absorbing boundary and in the presence of a parabolic barrier along one direction. By taking those of a…