Related papers: Exponential Mixing for Stochastic PDEs: The Non-Ad…
A fully discrete approximation of the one-dimensional stochastic heat equation driven by multiplicative space-time white noise is presented. The standard finite difference approximation is used in space and a stochastic exponential method…
In this paper we construct a framework for doing statistical inference for discretely observed stochastic differential equations (SDEs) where the driving noise has 'memory'. Classical SDE models for inference assume the driving noise to be…
In this paper we consider stochastic Fokker-Planck Partial Differential Equations (PDEs), obtained as the mean-field limit of weakly interacting particle systems subjected to both independent (or idiosyncratic) and common Brownian noises.…
The goal of this paper is twofold. In the first part we will study L\'{e}vy white noise in different distributional spaces and solve equations of the type $p(D)s=q(D)\dot{L}$, where $p$ and $q$ are polynomials. Furthermore, we will study…
Efficient simulation of stochastic partial differential equations (SPDE) on general domains requires noise discretization. This paper employs piecewise linear interpolation of noise in a fully discrete finite element approximation of a…
In this paper, we investigate the stochastic evolution equations (SEEs) driven by $\log$-Whittle-Mat$\acute{{\mathrm{e}}}$rn (W-M) random diffusion coefficient field and $Q$-Wiener multiplicative force noise. First, the well-posedness of…
We introduce the notion of stochastic logarithmic Lipschitz constants and use these constants to characterize stochastic contractivity of It\^o stochastic differential equations (SDEs) with multiplicative noise. We find an upper bound for…
We establish a Freidlin-Wentzell type large deviation principle (LDP) for a class of stochastic partial differential equations with locally monotone coefficients driven by L\'evy noise. Our results essentially improve a recent work on this…
A parameter estimation problem is considered for a linear stochastic hyperbolic equation driven by additive space-time Gaussian white noise. The damping/amplification operator is allowed to be unbounded. The estimator is of spectral type…
We investigate the longtime behavior of stochastic partial differential equations (SPDEs) with differential operators that depend on time and the underlying probability space. In particular, we consider stochastic parabolic evolution…
We consider the long-time behavior of an explicit tamed exponential Euler scheme applied to a class of parabolic semilinear stochastic partial differential equations driven by additive noise, under a one-sided Lipschitz continuity…
The article studies non-Gaussian extensions of a recently discovered link between certain Gaussian random fields, expressed as solutions to stochastic partial differential equations (SPDEs), and Gaussian Markov random fields. The focus is…
In this paper, we study a class of stochastic partial differential equations (SPDEs) driven by space-time fractional noises. Our method consists in studying first the nonlocal SPDEs and showing then the convergence of the family of these…
We apply the paracontrolled calculus to study the asymptotic behavior of a certain quasilinear PDE with smeared mild noise, which originally appears as the space-time scaling limit of a particle system in random environment on one…
An effective approach to modeling non-Markovian quantum systems is to embed a principal (quantum) system of interest into a larger quantum system. A widely employed embedding is one that uses another quantum system, referred to as the…
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…
This article investigates time-discrete approximations of Allen-Cahn type SPDEs driven by space-time white noise near the sharp interface limit $\epsilon\to 0$, where the small parameter $\epsilon$ is the diffuse interface thickness. We…
We establish the existence and uniqueness of strong solutions to stochastic porous media equations driven by L\'{e}vy noise on a $\sigma$-finite measure space $(E,\mathcal{B}(E),\mu)$, and with the Laplacian replaced by a negative definite…
We investigate the mixing properties of solutions to the stochastic transport equation $d u= \circ d W \cdot\nabla u$, where the driving noise $W(t,x)$ is white in time, colored and divergence-free in space. Furthermore, we prove the…
We establish the $L_p$-regularity theory for a semilinear stochastic partial differential equation with multiplicative white noise: $$ du = (a^{ij}u_{x^ix^j} + b^{i}u_{x^i} + cu + \bar b^{i}|u|^\lambda u_{x^i})dt + \sigma^k(u)dw_t^k,\quad…