Related papers: Effective action for stochastic partial differenti…
We introduce 'single-particle-exact density functional theory' (1pEx-DFT), a novel density functional approach that represents all single-particle contributions to the energy with exact functionals. Here, we parameterize interaction energy…
We investigate synchronization by noise for stochastic differential equations (SDEs) driven by a fractional Brownian motion (fbm) with Hurst index $H\in(0,1)$. Provided that the SDE has a negative top Lyapunov exponent, we show that a weak…
We develop a complete and rigorous mathematical framework for the analysis of stochastic neural field equations under the influence of spatially extended additive noise. By comparing a solution to a fixed deterministic front profile it is…
This paper develops a fractional stochastic partial differential equation (SPDE) to model the evolution of a random tangent vector field on the unit sphere. The SPDE is governed by a fractional diffusion operator to model the L\'{e}vy-type…
We present an abstract concept for the error analysis of numerical schemes for semilinear stochastic partial differential equations (SPDEs) and demonstrate its usefulness by proving the strong convergence of a Milstein-Galerkin finite…
The paper proposes a systematic framework for building data-driven stochastic differential equation (SDE) models from sparse, noisy observations. Unlike traditional parametric approaches, which assume a known functional form for the drift,…
We consider the family of stochastic partial differential equations indexed by a parameter $\eps\in(0,1]$, \begin{equation*} Lu^{\eps}(t,x) = \eps\sigma(u^\eps(t,x))\dot{F}(t,x)+b(u^\eps(t,x)), \end{equation*} $(t,x)\in(0,T]\times\Rd$ with…
By using Malliavin calculus, explicit derivative formulae are established for a class of semi-linear functional stochastic partial differential equations with additive or multiplicative noise. As applications, gradient estimates and Harnack…
In this paper, we provide a continuum model for the fluctuations of the symmetric simple exclusion process about its hydrodynamic limit. The model is based on an approximating sequence of stochastic PDEs with nonlinear, conservative noise.…
We propose a methodology to address two analysis problems concerning complex systems, namely bounding state functionals of stochastic differential equations (SDEs) and verifying set avoidance of systems described by partial differential…
Motivated by the modeling of the spatial structure of the velocity field of three-dimensional turbulent flows, and the phenomenology of cascade phenomena, a linear dynamics has been recently proposed able to generate high velocity gradients…
With a finite amount of measurement data acquired in variational quantum algorithms, the statistical benefits of several optimized numerical estimation schemes, including the scaled parameter-shift (SPS) rule and finite-difference (FD)…
In this paper, we consider the classical spin systems on unbounded lattices given by infinite-dimensional stochastic differential equations (SDEs). We assume that the stochastic forcing acts only on one particle. The other particles are not…
Non-local reaction-diffusion partial differential equations (PDEs) involving the fractional Laplacian have arisen in a wide variety of applications. One common tool to analyse the dynamics of classical local PDEs near instability is to…
In this paper we obtain Gaussian-type lower bounds for the density of solutions to stochastic differential equations (SDEs) driven by a fractional Brownian motion with Hurst parameter $H$. In the one-dimensional case with additive noise,…
A new method for solving numerically stochastic partial differential equations (SPDEs) with multiple scales is presented. The method combines a spectral method with the heterogeneous multiscale method (HMM) presented in [W. E, D. Liu, and…
Several relevant aspects of quantum-field processes can be well described by semiclassical methods. In particular, the knowledge of non-trivial classical solutions of the field equations, and the thermal and quantum fluctuations around…
In this paper we propose an all-in-one statement which includes existence, uniqueness, regularity, and numerical approximations of mild solutions for a class of stochastic partial differential equations (SPDEs) with non-globally monotone…
We consider stochastic partial differential equations on $\mathbb{R}^{d}, d\geq 1$, driven by a Gaussian noise white in time and colored in space, for which the pathwise uniqueness holds. By using the Skorokhod representation theorem we…
In this paper, we study a class of stochastic differential equations with additive noise that contains a fractional Brownian motion (fBM) and a Poisson point process of class (QL). The differential equation of this kind is motivated by the…