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We study a nonlinear, pseudomonotone, stochastic diffusion-convection evolution problem on a bounded spatial domain, in any space dimension, with homogeneous boundary conditions and reflection. The additive noise term is given by a…

Analysis of PDEs · Mathematics 2024-12-24 Niklas Sapountzoglou , Yassine Tahraoui , Guy Vallet , Aleksandra Zimmermann

We adopt a stochastic approach to study the charge transport in transistors. In this approach, the hole and electron densities are ruled by diffusion-reaction stochastic partial differential equations satisfying local detailed balance…

Statistical Mechanics · Physics 2025-06-17 Jiayin Gu

The wave speed of a stochastic wave equation driven by Riesz noise on the unbounded multidimensional spatial domain is estimated based on discrete measurements. Central limit theorems for second-order variations of the observations in…

Statistics Theory · Mathematics 2026-02-05 Anton Tiepner , Mathias Trabs , Eric Ziebell

In this paper we aim at characterizing the effect of stochastic fluctuations on the distribution of the energy exchanged by a quantum system with an external environment under sequences of quantum measurements performed at random times.…

Collapse models postulate that space is filled with a collapse noise field, inducing quantum Brownian motions which are dominant during the measurement, thus causing collapse of the wave function. An important manifestation of collapse…

Quantum Physics · Physics 2018-05-23 Mohammad Bahrami

We study the effect of thermal noise on the propagation speed of a planar flame. We show that this out of equilibrium greatly amplifies the effect of thermal noise to yield macroscopic reductions in the flame speed over what is predicted by…

Fluid Dynamics · Physics 2016-10-26 Hongliang Liu , Jonathan Goodman

We find the weak rate of convergence of the spatially semidiscrete finite element approximation of the nonlinear stochastic heat equation. Both multiplicative and additive noise is considered under different assumptions. This extends an…

Numerical Analysis · Mathematics 2016-03-15 Adam Andersson , Stig Larsson

In this paper, we investigate stochastic partial differential equations driven by multi-parameter anisotropic fractional Levy noises, including the stochastic Poisson equation, the linear heat equation, and the quasi-linear heat equation.…

Probability · Mathematics 2014-10-07 Xuebin Lu , Wanyang Dai

We explore the relation between fast waves, damping and imposed noise for different scalings by considering the singularly perturbed stochastic nonlinear wave equations \nu u_{tt}+u_t=\D u+f(u)+\nu^\alpha\dot{W} on a bounded spatial domain.…

Analysis of PDEs · Mathematics 2011-09-15 Wei Wang , Yan Lv , A. J. Roberts

In this paper we consider a system of non-linear stochastic heat equations on $\mathbb{R}^d$ driven by a Gaussian noise which is white in time and has a homogeneous spatial covariance. Under some suitable regularity and non degeneracy…

Probability · Mathematics 2016-07-06 Yinghui Shi , Xiaobin Sun

We define power variation estimators for the drift parameter of the stochastic heat equation with the fractional Laplacian and an additive Gaussian noise which is white in time and white or correlated in space. We prove that these…

Probability · Mathematics 2019-12-18 Zeina Mahdi Khalil , Ciprian Tudor

In this paper, we apply a recently developed nonparametric modeling approach, the "diffusion forecast", to predict the time-evolution of Fourier modes of turbulent dynamical systems. While the diffusion forecasting method assumes the…

Chaotic Dynamics · Physics 2016-03-23 Tyrus Berry , John Harlim

We consider non-parametric Bayesian estimation of the drift coefficient of a one-dimensional stochastic differential equation from discrete-time observations on the solution of this equation. Under suitable regularity conditions that are…

Statistics Theory · Mathematics 2014-07-15 Shota Gugushvili , Peter Spreij

We consider the problem of nonparametric estimation of the drift and diffusion coefficients of a Stochastic Differential Equation (SDE), based on $n$ independent replicates $\left\{X_i(t)\::\: t\in [0,1]\right\}_{1 \leq i \leq n}$, observed…

Statistics Theory · Mathematics 2023-11-28 Neda Mohammadi , Leonardo Santoro , Victor M. Panaretos

We consider change point detection for the volatility in second order linear parabolic stochastic partial differential equations based on high frequency spatio-temporal data. We give a test statistic to detect changes in the volatility…

Statistics Theory · Mathematics 2025-12-02 Yozo Tonaki , Yusuke Kaino , Masayuki Uchida

Wave propagation problems have many applications in physics and engineering, and the stochastic effects are important in accurately modeling them due to the uncertainty of the media. This paper considers and analyzes a fully discrete finite…

Numerical Analysis · Mathematics 2021-06-30 Yukun Li , Shuonan Wu , Yulong Xing

We consider nonparametric invariant density and drift estimation for a class of multidimensional degenerate resp. hypoelliptic diffusion processes, so-called stochastic damping Hamiltonian systems or kinetic diffusions, under anisotropic…

Statistics Theory · Mathematics 2022-05-24 Niklas Dexheimer , Claudia Strauch

We use an effective Markovian description to study the long-time behaviour of a nonlinear second order Langevin equation with Gaussian noise. When dissipation is neglected, the energy of the system grows as with time a power-law with an…

Chaotic Dynamics · Physics 2014-12-19 Kirone Mallick

We study the effect of Gaussian perturbations on a class of model hyperbolic partial differential equations with double symplectic characteristics in low spatial dimensions, extending some recent work in [5]. The coefficients of our partial…

Probability · Mathematics 2024-09-04 Enrico Bernardi , Leonardo Marconi

We construct a positivity-preserving Lie--Trotter splitting scheme with finite difference discretization in space for approximating the solutions to a class of nonlinear stochastic heat equations with multiplicative space-time white noise.…

Numerical Analysis · Mathematics 2023-02-20 Charles-Edouard Bréhier , David Cohen , Johan Ulander