相关论文: On a modelled rough heat equation

We consider a Stratonovich heat equation in $(0,1)$ with a nonlinear multiplicative noise driven by a trace-class Wiener process. First, the equation is shown to have a unique mild solution. Secondly, convolutional rough paths techniques…

We consider differential equations driven by rough paths and study the regularity of the laws and their long time behavior. In particular, we focus on the case when the driving noise is a rough path valued fractional Brownian motion with…

This paper studies the stochastic heat equation with multiplicative noises of the form uW, where W is a mean zero Gaussian noise and the differential element uW is interpreted both in the sense of Skorohod and Stratonovich. The existence…

Here, we provide a unified framework for numerical analysis of stochastic nonlinear fractional diffusion equation driven by fractional Gaussian noise with Hurst index $H\in(0,1)$. A novel estimate of the second moment of the stochastic…

We investigate the existence and regularity of the local times of the solution to a linear system of stochastic wave equations driven by a Gaussian noise that is fractional in time and colored in space. Using Fourier analytic methods, we…

Modeling turbulent flows by a random Fourier decomposition is a classical procedure in order to use simplified models of turbulence in heat transport and other applications. We carefully investigate the Fourier time series of…

In this article we present a {\it quantitative} central limit theorem for the stochastic fractional heat equation driven by a a general Gaussian multiplicative noise, including the cases of space-time white noise and the white-colored noise…

We study the law of the solution to the stochastic heat equation with additive Gaussian noise which behaves as the fractional Brownian motion in time and is white in space. We prove a decomposition of the solution in terms of the…

In this paper, we study the backward problem of determining initial condition for some class of nonlinear parabolic equations in multidimensional domain where data are given under random noise. This problem is ill-posed, i.e., the solution…

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…

In this paper, we establish a version of the Feynman-Kac formula for multidimensional stochastic heat equation driven by a general semimartingale. This Feynman-Kac formula is then applied to study some nonlinear stochastic heat equations…

We study a two-dimensional incompressible vorticity equation on the torus driven by transport-type fractional Brownian noise with Hurst parameter $H \in (1/2,1)$. The model captures persistent, long-range correlated forcing consistent with…

In this paper, a Feynman-Kac formula is established for stochastic partial differential equation driven by Gaussian noise which is, with respect to time, a fractional Brownian motion with Hurst parameter $H<1/2$. To establish such a…

We study the heat equation with a random potential term. The potential is a one-sided stable noise, with positive jumps, which does not depend on time. To avoid singularities, we define the equation in terms of a construction similar to the…

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…

Harmonic balance (HB) is a popular Fourier-Galerkin method used in the analysis of nonlinear vibration problems where dynamical systems are subjected to periodic forcing. We adapt HB to find the periodic steady-state response of nonlinear…

Shear localization occurs in various instances of material instability in solid mechanics and is typically associated with Hadamard-instability for an underlying model. While Hadamard instability indicates the catastrophic growth of…

In this paper, we investigate the averaging principle for a class of semilinear slow-fast partial differential equations driven by finite-dimensional rough multiplicative noise. Specifically, the slow component is driven by a general random…

We study a model that intermediates among the wave, heat, and transport equations. The approach considers the propagation of initial disturbances in a one-dimensional medium that can vibrate. The medium is nonlinear in such a form that…

We present sufficient conditions for finite controlled rho-variation of the covariance of Gaussian processes with stationary increments, based on concavity or convexity of their variance function. The motivation for this type of conditions…