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In this paper, we present a rate of convergence in the uniform norm for the densities of spatial averages of the solution to the d-dimensional parabolic Anderson model driven by a Gaussian multiplicative noise, which is white in time and…

Probability · Mathematics 2022-05-30 Sefika Kuzgun , David Nualart

We consider the linear stochastic heat and wave equations with generalized Gaussian noise that is white in time and spatially correlated. Under the assumption that the homogeneous spatial correlation $f$ satisfies some mild conditions, we…

Probability · Mathematics 2021-01-26 Jaeyun Yi

We consider Gaussian Laplace eigenfunctions on the two-dimensional flat torus (arithmetic random waves), and provide explicit Berry-Esseen bounds in the 1-Wasserstein distance for the normal and non-normal high-energy approximation of the…

Probability · Mathematics 2017-02-14 Giovanni Peccati , Maurizia Rossi

In this paper, we obtain the existence and uniqueness of the strong solution to one spatial dimension stochastic wave equation $\frac{\partial^2 u(t,x)}{\partial t^2}=\frac{\partial^2 u(t,x)}{\partial x^2}+\sigma(t,x,u(t,x))\dot{W}(t,x)$…

Probability · Mathematics 2021-10-27 Shuhui Liu , Yaozhong Hu , Xiong Wang

We derive first-order (in the stepsize) bounds on the bias in Wasserstein distances of the invariant measure of stochastic gradient kinetic Langevin dynamics with minimal assumptions on the stochastic gradient noise. These bounds sharpen…

Computation · Statistics 2026-04-28 Daniel Paulin , Peter A. Whalley

Euler integrals of deterministic functions have recently been shown to have a wide variety of possible applications, including in signal processing, data aggregation and network sensing. Adding random noise to these scenarios, as is natural…

Probability · Mathematics 2015-06-30 Gregory Naitzat , Robert J. Adler

In this work, we obtain the central limit theorem for fluctuations of Young diagrams around their limit shape in the bulk of the "spectrum" of partitions of a large integer n (under the Plancherel measure). More specifically, we show that,…

Probability · Mathematics 2007-05-23 L. V. Bogachev , Z. G. Su

We consider an open model possessing a Markovian quantum stochastic limit and derive the limit stochastic Schrodinger equations for the wave function conditioned on indirect observations using only the von Neumann projection postulate. We…

Quantum Physics · Physics 2007-05-23 John Gough , Andrei Sobolev

We discuss Einstein-Klein-Gordon system in an environment of an infinite number of scalar fields leading to an external thermal noise. In the lowest order of metric and field perturbations the quadratic fluctuations consist of a sum of…

General Relativity and Quantum Cosmology · Physics 2019-05-22 Z. Haba

Non-Gaussian noise is omnipresent in systems where the central-limit theorem is inapplicable. We here investigate the stochastic thermodynamics of small systems that are described by a general Kramers-Moyal equation that includes both…

Statistical Mechanics · Physics 2025-02-28 Arthur M. Faria , Marcus V. S. Bonanca , Eric Lutz

In this paper, we analyze Galerkin approximations for stochastic evolution equations driven by an additive Gaussian noise which is temporally white and spatially fractional with Hurst index less than or equal to $1/2$. First we regularize…

Numerical Analysis · Mathematics 2020-06-08 Yanzhao Cao , Jialin Hong , Zhihui Liu

We construct Langevin equations describing the fluctuations of the tensor order parameter $Q_{\alpha\beta}$ in nematic liquid crystals by adding noise terms to time-dependent variational equations that follow from the Ginzburg-Landau-de…

Soft Condensed Matter · Physics 2010-01-07 A. K. Bhattacharjee , Gautam I. Menon , R. Adhikari

For the $1+1$ dimensional nonlinear damped stochastic Klein-Gordon equation driven by space-time white noise, we prove that the second-order increments of the solution can be approximated, after scaling with the diffusion coefficient, by…

Probability · Mathematics 2026-01-13 Guanglin Rang , Ran Wang

We provide an abstract multivariate central limit theorem with the Lindeberg-type error bounded in terms of Lipschitz functions (Wasserstein 1-distance) or functions with bounded second or third derivatives. The result is proved by means of…

Probability · Mathematics 2019-01-03 Martin Raič

Stochastic Navier-Stokes equations in 2D and 3D possibly unbounded domains driven by a multiplicative Gaussian noise are considered. The noise term depends on the unknown velocity and its spatial derivatives. The existence of a martingale…

Probability · Mathematics 2017-01-03 Zdzisław Brzeźniak , Elżbieta Motyl

We present a way to use Stein's method in order to bound the Wasserstein distance of order $2$ between two measures $\nu$ and $\mu$ supported on $\mathbb{R}^d$ such that $\mu$ is the reversible measure of a diffusion process. In order to…

Probability · Mathematics 2018-06-25 Thomas Bonis

We introduce a stochastic partial differential equation (SPDE) with elliptic operator in divergence form, with measurable and bounded coefficients and driven by space-time white noise. Such SPDEs could be used in mathematical modelling of…

Probability · Mathematics 2020-01-09 Mounir Zili , Eya Zougar

We consider Canonical Gibbsian ensembles of Euler point vortices on the 2-dimensional torus or in a bounded domain of R 2 . We prove that under the Central Limit scaling of vortices intensities, and provided that the system has zero global…

Probability · Mathematics 2020-04-22 Francesco Grotto , Marco Romito

Non-reciprocal systems can be thought of as disobeying Newtons third law - an action does not cause an equal and opposite reaction. In recent years there has been a dramatic rise in interest towards such systems. On a fundamental level,…

Statistical Mechanics · Physics 2024-12-06 Sergei Shmakov , Glasha Osipycheva , Peter B. Littlewood

We establish the convergence of the densities of a sequence of nonlinear functionals of an underlying Gaussian process to the density of a Gamma distribution. The key idea of our work is a new density formula for random variables in the…

Probability · Mathematics 2025-11-17 Solesne Bourguin , Thanh Dang , Yaozhong Hu