相关论文: Characterization of the support for Wick powers of…

The average thermodynamic power of a time-dependent external potential in the white-noise Langevin model is derived using a Green's function solution. The power appears as a driving term in the differential equation for the average energy…

We study the solutions of the stochastic heat equation with multiplicative space-time white noise. We prove a comparison theorem between the solutions of stochastic heat equations with the same noise coefficient which is H\"{o}lder…

We prove a Stroock-Varadhan's type support theorem for a stochastic partial differential equation (SPDE) on the real line with a noise term driven by a cylindrical Wiener process on $L_2 (\mathbb{R})$. The main ingredients of the proof are…

We establish a version of the Feynman-Kac formula for the multidimensional stochastic heat equation with a multiplicative fractional Brownian sheet. We use the techniques of Malliavin calculus to prove that the process defined by the…

We consider the fractional stochastic heat equation on the $d$-dimensional torus $\mathbb{T}^d:=\left[-\frac{1}{2},\frac{1}{2}\right]^d$, $d\geq 1$, with periodic boundary conditions: \[ \partial_t u(t,\textbf{x})=…

We prove that the weight polytope of the Hurwitz form of a polarized smooth toric variety coincides with the convex hull of the characteristic vectors introduced in the previous work of Ogusu and the author with respect to all regular…

In this article, we consider the quasi-linear stochastic wave and heat equations on the real line and with an additive Gaussian noise which is white in time and behaves in space like a fractional Brownian motion with Hurst index $H\in…

This is a preliminary announcement of results in the PhD. thesis of the first author concerning the nonlinear stochastic heat equation in the spatial domain $\R$, driven by space-time white noise. A central special case is the parabolic…

We study the solutions of the stochastic heat equation driven by spatially inhomogeneous multiplicative white noise based on a fractal measure. We prove pathwise uniqueness for solutions of this equation when the noise coefficient is…

In this article, we address the velocity tracking control problem for a class of stochastic non-Newtonian fluids. More precisely, we consider the stochastic third-grade fluid equation perturbed by infinite-dimensional additive white noise…

We consider the stochastic heat equation whose solution is observed discretely in space and time. An asymptotic analysis of power variations is presented including the proof of a central limit theorem. It generalizes the theory from…

We study the Gaussian fluctuations of a nonlinear stochastic heat equation in spatial dimension two. The equation is driven by a Gaussian multiplicative noise. The noise is white in time, smoothed in space at scale $\varepsilon$, and tuned…

We consider a stochastic extension of the nonlocal convective Cahn-Hilliard equation containing an additive Wiener process noise. We first introduce a suitable analytical setting and make some mathematical and physical assumptions. We then…

We consider nonlinear parabolic SPDEs of the form $\partial_t u=-(-\Delta)^{\alpha/2} u + b(u) +\sigma(u)\dot w$, where$\dot w$ denotes space-time white noise. The functions $b$ and $\sigma$ are both locally Lipschitz continuous. Under some…

We investigate the properties of the Wick square of Gaussian white noises through a new method to perform non linear operations on Hida distributions. This method lays in between the Wick product interpretation and the usual definition of…

Recently, a number of authors have investigated the conditions under which a stochastic perturbation acting on an infinite dimensional dynamical system, e.g. a partial differential equation, makes the system ergodic and mixing. In…

We prove global in time well-posedness for perturbations of the 2D stochastic Navier-Stokes equations \begin{equation*} \partial_t u + u \cdot \nabla u = \Delta u - \nabla p + \zeta + \xi \;, \quad u (0, \cdot) = u_{0}(\cdot) \;, \quad…

Upon its inception the theory of regularity structures allowed for the treatment for many semilinear perturbations of the stochastic heat equation driven by space-time white noise. When the driving noise is non-Gaussian the machinery of…

We propose a time-implicit, finite-element based space-time discretization of the necessary and sufficient optimality conditions for the stochastic linear-quadratic optimal control problem with the stochastic heat equation driven by linear…

We consider the linear stochastic wave equation with spatially homogenous Gaussian noise, which is fractional in time with index $H>1/2$. We show that the necessary and sufficient condition for the existence of the solution is a relaxation…