Related papers: Stochastic velocity motions and processes with ran…
Iterated Bessel processes R^\gamma(t), t>0, \gamma>0 and their counterparts on hyperbolic spaces, i.e. hyperbolic Brownian motions B^{hp}(t), t>0 are examined and their probability laws derived. The higher-order partial differential…
In this paper, we study univariate and planar random motions with variable propagation speeds. We first consider motions with space-varying velocity, which can be reduced to constant-velocity motions by means of suitable nonlinear…
The motion of overdamped particles in a one-dimensional spatially-periodic potential is considered. The potential is also randomly-fluctuating in time, due to multiplicative colored noise terms, and has a deterministic tilt. Numerical…
We study the motion of a massive particle in a quenched random environment at zero temperature. The distribution of particle positions is investigated numerically and special focus is placed on the mean stopping distance and its…
The dynamics of particles moving in a medium defined by its relativistically invariant stochastic properties is investigated. For this aim, the force exerted on the particles by the medium is defined by a stationary random variable as a…
In the case of a rarefaction fan in a non-stationary Hammersley process, we explicitly calculate the asymptotic behavior of the process as we move out along a ray, and the asymptotic distribution of the angle within the rarefaction fan of a…
The transport equation of active motion is generalised to consider time-fractional dynamics for describing the anomalous diffusion of self-propelled particles observed in many different systems. In the present study, we consider an…
Levy walk at the finite velocity is considered. To analyze the spatial and temporal characteristics of this process, the method of moments has been used. The asymptotic distributions of the moments (at $t\to\infty$) have been obtained for…
It has been noticed that when the waiting time distribution exhibits a transition from an intermediate time power law decay to a long-time exponential decay in the continuous time random walk model, a transition from anomalous diffusion to…
Mathematical models of motility are often based on random-walk descriptions of discrete individuals that can move according to certain rules. It is usually the case that large masses concentrated in small regions of space have a great…
The two--dimensional diffusive dynamics of test particles in a random electromagnetic field is studied. The synthetic electromagnetic fluctuations are generated through randomly placed magnetised ``clouds'' oscillating with a frequency…
We study a system of particles moving on a line in the same direction. Passing is allowed and when a fast particle overtakes a slow particle, it acquires a new velocity drawn from a distribution P_0(v), while the slow particle remains…
U-statistics of spatial point processes given by a density with respect to a Poisson process are investigated. In the first half of the paper general relations are derived for the moments of the functionals using kernels from the Wiener-Ito…
Consider a system performing a continuous-time random walk on the integers, subject to catastrophes occurring at constant rate, and followed by exponentially-distributed repair times. After any repair the system starts anew from state zero.…
A simple model for the nonlinear collective transport of interacting particles in a random medium with strong disorder is introduced and analyzed. A finite threshold for the driving force divides the behavior into two regimes characterized…
A wide range of physical problems can be described by randomly-oriented linear trajectories, including any system of objects, organisms, particles, or rays that follow a linear path. Dependent upon the particular random variables that…
As a first step toward a characterization of the limiting extremal process of branching Brownian motion, we proved in a recent work [Comm. Pure Appl. Math. 64 (2011) 1647-1676] that, in the limit of large time $t$, extremal particles…
In this article, the following results are obtained: the process of a randomly wandering particle having a size and a continuous trajectory of motion is considered; (b) based on the study of this probabilistic process, a derivation of the…
The mobility of an overdamped particle, in a periodic potential tilted by a constant external field and moving in a medium with periodic friction coefficient is examined. When the potential and the friction coefficient have the same…
We consider the telegraph process with two velocities, $a_1>a_2\in\mathbb{R}$, and two rates of reversal, $\lambda_1,\lambda_2>0$. We study some of its features with respect to the conditional probability measure where both the initial…