Related papers: Gaussian convergence for stochastic acceleration o…
We consider the motion of a particle governed by a weakly random Hamiltonian flow. We identify temporal and spatial scales on which the particle trajectory converges to a spatial Brownian motion. The main technical issue in the proof is to…
We study a diffusion approximation for a model of stochastic motion of a particle in one spatial dimension. The velocity of the particle is constant but the direction of the motion undergoes random changes with a Poisson clock. Moreover,…
We prove a local limit theorem, i.e. a central limit theorem for densities, for a sequence of independent and identically distributed random variables taking values on an abstract Wiener space; the common law of those random variables is…
The specification of a covariance function is of paramount importance when employing Gaussian process models, but the requirement of positive definiteness severely limits those used in practice. Designing flexible stationary covariance…
An efficient algorithm to simulate dynamics of open quantum system is presented. The method describes the dynamics by unraveling stochastic wave functions converging to a density operator description. The stochastic techniques are based on…
New results on uniform convergence in probability for expansions of Gaussian random processes using compactly supported wavelets are given. The main result is valid for general classes of nonstationary processes. An application of the…
We consider uniform moment convergence of lag-window spectral density estimates for univariate and multivariate stationary processes. Optimal rates of convergence are obtained under mild and easily verifiable conditions. Our theory…
We show, for a class of discrete Fleming-Viot (or Moran) type particle systems, that the convergence to the equilibrium is exponential for a suitable Wassertein coupling distance. The approach provides an explicit quantitative estimate on…
Dynamical systems of N particles in \R^{D} interacting by a singular pair potential of mean field type are considered. The systems are assumed to be of gradient type and the existence of a macroscopic limit in the many particle limit is…
We consider a one-dimensional aggregation-diffusion equation, which is the gradient flow in the Wasserstein space of a functional with competing attractive-repulsive interactions. We prove that the fully deterministic particle…
The first passage time density of a diffusion process to a time varying threshold is of primary interest in different fields. Here we consider a Brownian motion in presence of an exponentially decaying threshold to model the neuronal…
The time dependence of one-dimensional quantum mechanical probability densities is presented when the potential in which a particle moves is suddenly changed, called a quench. Quantum quenches are mainly addressed but a comparison with…
We consider the acceleration of charged particles in relativistic shearing flows, with Lorentz factor up to $\Gamma_0 \sim 20$. We present numerical solutions to the particle transport equation and compare these with results from analytical…
We study rates of convergence in central limit theorems for the partial sum of squares of general Gaussian sequences, using tools from analysis on Wiener space. No assumption of stationarity, asymptotically or otherwise, is made. The main…
In this paper, we construct a type of interacting particle systems to approximate a class of stochastic different equations whose coefficients depend on the conditional probability distributions of the processes given partial observations.…
Gaussian particles provide a flexible framework for modelling and simulating three-dimensional star-shaped random sets. In our framework, the radial function of the particle arises from a kernel smoothing, and is associated with an…
We study a one-dimensional model for heavy particles in a compressible fluid. The fluid-velocity field is modelled by a persistent Gaussian random function, and the particles are assumed to be weakly inertial. Since one-dimensional…
Passive scalar equation is considered in a turbulent homogeneous incompressible Gaussian velocity field. The turbulent nature of the field results in non-smooth coefficients in the equation. A strong, in the stochastic sense, solution of…
We model the diffusive shock acceleration of particles in a system of two colliding shock waves and present a method to solve the time-dependent problem analytically in the test-particle approximation and high energy limit. In particular,…
We address the problem of the so-called ``granular gases'', i.e. gases of massive particles in rapid movement undergoing inelastic collisions. We introduce a class of models of driven granular gases for which the stationary state is the…