相关论文: Superdiffusive Central Limit Theorem for the Stoch…

Smoothed Particle Hydrodynamics (SPH_ is a mesh-free Lagrangian method renowned for modeling large deformations and free-surface flows, yet classical formulations remain confined to deterministic systems. We introduce Stochastic SPH…

In this paper we study coupled fast-slow ordinary differential equations (ODEs) with small time scale separation parameter $\epsilon$ such that, for every fixed value of the slow variable, the fast dynamics are sufficiently chaotic with…

We consider the stochastic heat equation $\partial_tZ= \partial_x^2 Z - Z \dot W$ on the real line, where $\dot W$ is space-time white noise. $h(t,x)=-\log Z(t,x)$ is interpreted as a solution of the KPZ equation, and $u(t,x)=\partial_x…

This work aims at making a comprehensive contribution in the general area of parametric inference for discretely observed diffusion processes. Established approaches for likelihood-based estimation invoke a time-discretisation scheme for…

Recent years have witnessed significant progress in developing effective training and fast sampling techniques for diffusion models. A remarkable advancement is the use of stochastic differential equations (SDEs) and their…

This paper extends deterministic notions of Strong Stability Preservation (SSP) to the stochastic setting, enabling nonlinearly stable numerical solutions to stochastic differential equations (SDEs) and stochastic partial differential…

In this article we derive rigorously amplitude equations for stochastic PDEs with quadratic nonlinearities, under the assumption that the noise acts only on the stable modes and for an appropriate scaling between the distance from…

The area enclosed by the two-dimensional Brownian motion in the plane was studied by L\'evy, who found the characteristic function and probability density of this random variable. For other planar processes, in particular ergodic diffusions…

We study a class of nonlinear Burgers-type stochastic partial differential equations driven by additive space-time white noise in one spatial dimension. Building on the rough path framework initiated by Hairer, which provides a pathwise…

The object of this paper is a one-dimensional generalized porous media equation (PDE) with possibly discontinuous coefficient $\beta$, which is well-posed as an evolution problem in $L^1(\mathbb{R})$. In some recent papers of Blanchard et…

In this article, we show how the theory of rough paths can be used to provide a notion of solution to a class of nonlinear stochastic PDEs of Burgers type that exhibit too high spatial roughness for classical analytical methods to apply. In…

We derive from a class of microscopic asymmetric interacting particle systems on ${\mathbb Z}$, with long range jump rates of order $|\cdot|^{-(1+\alpha)}$ for $0<\alpha<2$, different continuum fractional SPDEs. More specifically, we show…

We propose a stochastic model predictive control (SMPC) framework for a broad class of unconstrained controlled stochastic differential equations (SDEs) and establish its mean-square exponential stability in the infinite-horizon limit. At…

A series of recent articles introduced a method to construct stochastic partial differential equations (SPDEs) which are invariant with respect to the distribution of a given conditioned diffusion. These works are restricted to the case of…

A version of the fundamental mean-square convergence theorem is proved for stochastic differential equations (SDE) which coefficients are allowed to grow polynomially at infinity and which satisfy a one-sided Lipschitz condition. The…

Ecological Momentary Assessment (EMA) studies enable the collection of high-frequency self-reports of suicidal thoughts and behaviors (STBs) via smartphones. Latent stochastic differential equations (SDEs) are a promising model class for…

Higher order fluctuation expansions for stochastic heat equations (SHE) with nonlinear, non-conservative and conservative noise are obtained. These Edgeworth-type expansions describe the asymptotic behavior of solutions in suitable joint…

The article focuses on error estimates as well as stability analysis of deep learning methods for stationary and non-stationary viscous Burgers equation in two and three dimensions. The local well-posedness of homogeneous boundary value…

We introduce the stochastic Boltzmann equation (SBE) as an approach for exploring the spin dynamics of magnetic molecules coupled to a stochastic environment. The SBE is a time-evolution equation for the probability density of the spin…

This paper develops and analyzes a fully discrete finite element method for a class of semilinear stochastic partial differential equations (SPDEs) with multiplicative noise. The nonlinearity in the diffusion term of the SPDEs is assumed to…