Related papers: Diffusion Means in Geometric Spaces
We establish diffusion and fractional Brownian motion approximations for motions in a Markovian Gaussian random field with a nonzero mean.
This paper presents a novel formula for the transition density of the Brownian motion on a sphere of any dimension and discusses an algorithm for the simulation of the increments of the spherical Brownian motion based on this formula. The…
We investigate the support of smeary, directionally smeary, and finite sample smeary probability measures $\mu$ with density $\rho$ on spheres $\mathbb{S}^m$. First, in the rotationally symmetric case, we show that a distribution is not…
Non-Gaussian shapes, despite a linear form of the mean-squared displacement, have been observed for the displacement distribution in a large range of diffusive systems. Stochastic models for such "Brownian yet non-Gaussian" diffusion will…
Three-dimensional Monte Carlo simulations provide a striking confirmation to a recent theoretical prediction: the Brownian non-Gaussian diffusion of critical self-avoiding walks. Although the mean square displacement of the polymer center…
We discuss the diffusion phenomenon in the parabolic and hyperbolic regimes. New effects related to the finite velocity of the diffusion process are predicted, that can partially explain the strange behavior associated to adsorption…
Diffusion models have achieved remarkable success in generating samples from unknown data distributions. Most popular stochastic differential equation-based diffusion models perturb the target distribution by adding Gaussian noise,…
Nonergodicity observed in single-particle tracking experiments is usually modeled by transient trapping rather than spatial disorder. We introduce models of a particle diffusing in a medium consisting of regions with random sizes and random…
Recent progresses in single particle tracking have shown evidences of non-Gaussian distribution of displacements in living cells, both near the cellular membrane and inside the cytoskeleton. A similar behavior has also been observed in…
This paper discusses the fractional diffusion equation forced by a tempered fractional Gaussian noise. The fractional diffusion equation governs the probability density function of the subordinated killed Brownian motion. The tempered…
Barrier crossing is a widespread phenomenon across natural and engineering systems. While an abundant cross-disciplinary literature on the topic has emerged over the years, the stochastic underpinnings of the process are yet to be linked…
Anomalous diffusion is an established phenomenon but still a theoretical challenge in non-equilibrium statistical mechanics. Physical models are built incrementally, and the most recent and most general family is based on the fractional…
The mechanism of diffusing diffusivity predicts that, in environments where the diffusivity changes gradually, the displacement distribution becomes non-Gaussian, even though the mean-squared displacement (MSD) grows linearly with time.…
We study the maximum likelihood estimator of the drift parameters of a stochastic differential equation, with both drift and diffusion coefficients constant on the positive and negative axis, yet discontinuous at zero. This threshold…
We introduce a new universality class of one-dimensional iteration model giving rise to self-similar motion, in which the Feigenbaum constants are generalized as self-similar rates and can be predetermined. The curves of the mean-square…
The effective diffusion of Brownian particles in periodic potential has been a central topic in nonequilibrium statistical physcis. A classical result is the Lifson formula which provides the effective diffusion constant in periodic…
The coupling between advection and diffusion in position space can often lead to enhanced mass transport compared to diffusion without flow. An important framework used to characterize the long-time diffusive transport in position space is…
We study the dynamics of a Brownian motion with a diffusion coefficient which evolves stochastically. We first study this process in arbitrary dimensions and find the scaling form and the corresponding scaling function of the position…
Based upon the Smoluchowski equation on curved manifolds three physical observables are considered for the Brownian displacement, namely, geodesic displacement, $s$, Euclidean displacement, $\delta{\bf R}$, and projected displacement…
Diffusion magnetic resonance imaging (dMRI) is a relatively modern technique used to study tissue microstructure in a non-invasive way. Non-Gaussian diffusion representation is related to the restricted diffusion and can provide information…