Related papers: Semilinear stochastic partial differential equatio…
We develop a solution theory in H\"older spaces for a quasilinear stochastic PDE driven by an additive noise. The key ingredients are two deterministic PDE Lemmas which establish a priori H\"older bounds for an equation with irregular right…
Constructing numerical models of noisy partial differential equations is very delicate. Our long term aim is to use modern dynamical systems theory to derive discretisations of dissipative stochastic partial differential equations. As a…
This paper is concerned with the large deviation principle of the non-local fractional stochastic reaction-diffusion equation with a polynomial drift of arbitrary degree driven by multiplicative noise defined on unbounded domains. We first…
We study a class of stochastic time-fractional equations on $\mathbb{R}^d$ driven by a centered Gaussian noise, involving a Caputo time derivative of order $\beta>0$, a fractional (power) Laplacian of order $\alpha>0$, and a…
This paper studies the behaviour of quadratic variations of a stochastic wave equation driven by a noise that is white in space and fractional in time. Complementing the analysis of quadratic variations in the space component carried out by…
In this article, we prove the Quantitative Central Limit Theorem (QCLT) for the spatial average of the solution of the nonlinear stochastic heat equation with constant initial condition, driven by space-time Gaussian white noise in…
We establish the moderate deviation principle for the solutions of a class of stochastic partial differential equations with non-Lipschitz continuous coefficients. As an application, we derive the moderate deviation principle for two…
In this paper, we consider a semi-linear stochastic strongly damped wave equation driven by additive Gaussian noise. Following a semigroup framework, we establish existence, uniqueness and space-time regularity of a mild solution to such…
In this article, we study a class of semilinear stochastic partial differential equations driven by an additive space time white noise. We establish Harnack inequalities for the semigroup associated with the solution by using coupling…
This paper establishes a functional stable central limit theorem for a class of superdiffusive solutions to stochastic differential equations driven by an $\alpha$-stable process.
In this article, we establish the Freidlin-Wentzell type large deviation principle and central limit theorem for stochastic fractional conservation laws with small multiplicative noise in kinetic formulation framework. The weak convergence…
Consider stochastic partial differential equations (SPDEs) with fully local monotone coefficients in a Gelfand triple $V\subseteq H\subseteq V^*$ $$ \left\{ \begin{align} &dX_t=A(t,X_t)dt+B(t,X_t)dW_t,\ t\in (0,T]\\\\& X_0=x\in H,…
Fix $d\in\{1,2\}$, we consider a $d$-dimensional stochastic wave equation driven by a Gaussian noise, which is temporally white and colored in space such that the spatial correlation function is integrable and satisfies Dalang's condition.…
We establish a central limit theorem and large deviations principle that characterises small noise fluctuations of the generalised Dean--Kawasaki stochastic PDE. The fluctuations agree to first order with fluctuations of certain interacting…
We study one-dimensional nonlinear stochastic cable equations driven by a multiplicative space-time white noise. Using the Malliavin-Stein method, we prove a central limit theorem for the spatial average of the solution. The convergence is…
We study the small noise asymptotic for stochastic Burgers equations on $(0,1)$ with Dirichlet boundary condition. We consider the case that the noise is more singular than space-time white noise. We let the noise magnitude $\sqrt{\epsilon}…
Here we establish the central limit theorem for a class of stochastic partial differential equations (SPDEs) and as an application derive this theorem for two widely studied population models known as super-Brownian motion and Fleming-Viot…
We introduce a stochastic partial differential equation (SPDE) with elliptic operator in divergence form, with measurable and bounded coefficients and driven by space-time white noise. Such SPDEs could be used in mathematical modelling of…
We introduce the uniqueness, existence, $L_p$-regularity, and maximal H\"older regularity of the solution to semilinear stochastic partial differential equation driven by a multiplicative space-time white noise: $$ u_t = au_{xx} + bu_{x} +…
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…