相关论文: Paracontrolled quasi-geostrophic equation with spa…
In this article, we study the stochastic wave equation on the entire space $\mathbb{R}^d$, driven by a space-time L\'evy white noise with possibly infinite variance (such as the $\alpha$-stable L\'evy noise). In this equation, the noise is…
We consider the Surface Quasi-Geostrophic equation (SQG) driven by space-time white noise and show the existence of a local in time solution by applying the theory of regularity structures. A main difficulty is the presence of…
We consider the stochastic damped nonlinear wave equation $\partial_t^{2}u+\partial_t u+u-\Delta u +u^{3} = \sqrt{2} {\langle{\nabla}\rangle^{-s}} \xi$ on the two-dimensional torus $\mathbb T^2$, where $\xi$ denotes a space-time white noise…
We establish an optimal strong convergence rate of a fully discrete numerical scheme for second order parabolic stochastic partial differential equations with monotone drifts, including the stochastic Allen-Cahn equation, driven by an…
This paper studies the linear stochastic partial differential equation of fractional orders both in time and space variables $\left(\partial^\beta + \frac{\nu}{2} (-\Delta)^{\alpha/2} \right) u(t,x)= \lambda u(t,x) \dot{W}(t,x)$, where…
We consider the strong numerical approximation for a fourth-order stochastic nonlinear SPDE driven by space-time white noise on $2$-dimensional torus. We consider its full discretisation with a spectral Galerkin scheme in space and Euler…
In this paper, we study a class of nonlinear space-time fractional stochastic kinetic equations in $\mathbb{R}^d$ with Gaussian noise which is white in time and homogeneous in space. This type of equation constitutes an extension of the…
We consider the homogenisation problem for the $\phi^4_2$ equation on the torus $\mathbb{T}^2$, namely the behaviour as $\varepsilon \to 0$ of the solutions to the equation suggestively written as $$ \partial_t u_\varepsilon - \nabla\cdot…
We show the global-in-time well-posedness of the complex Ginzburg-Landau (CGL) equation with a space-time white noise on the 3-dimensional torus. Our method is based on [14], where Mourrat and Weber showed the global well-posedness for the…
We consider the non-linear equation $T^{-1} u+\partial_tu-\partial_x^2\pi(u)=\xi$ driven by space-time white noise $\xi$, which is uniformly parabolic because we assume that $\pi'$ is bounded away from zero and infinity. Under the further…
We consider the Cauchy problem for a stochastic scalar parabolic-hyperbolic equation in any space dimension with nonlocal, nonlinear, and possibly degenerate diffusion terms. The equations are nonlocal because they involve fractional…
In this paper, we prove existence, uniqueness and regularity for a class of stochastic partial differential equations with a fractional Laplacian driven by a space-time white noise in dimension one. The equation we consider may also include…
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…
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…
Even though the heat equation with random potential is a well-studied object, the particular case of time-independent Gaussian white noise in one space dimension has yet to receive the attention it deserves. The paper investigates the…
We discrete the ergodic semilinear stochastic partial differential equations in space dimension $d \leq 3$ with additive noise, spatially by a spectral Galerkin method and temporally by an exponential Euler scheme. It is shown that both the…
The objective of the paper is to identify and investigate all possible types of asymptotic behavior for the maximum likelihood estimators of the unknown parameters in the second-order linear stochastic ordinary differential equation driven…
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…
We give necessary and/or sufficient conditions for stochastic stability of second-order linear autonomous systems with parameters, which are perturbed by a random process of the "white noise" type. The Ito's and Stratonovich's forms of…
The objective of this note is to present the results from the two recent papers. We study the Navier--Stokes equation on the two--dimensional torus when forced by a finite dimensional white Gaussian noise. We give conditions under which…