相关论文: Feynman--Kac formula for the heat equation driven …
In this paper we obtain a Feynman-Kac formula for the solution of a fractional stochastic heat equation driven by fractional noise. One of the main difficulties is to show the exponential integrability of some singular nonlinear functionals…
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…
This paper studies the stochastic heat equation driven by time fractional Gaussian noise with Hurst parameter $H\in(0,1/2)$. We establish the Feynman-Kac representation of the solution and use this representation to obtain matching lower…
This paper establishes a Feynman-Kac formula to represent the solution to general time inhomogeneous stochastic parabolic partial differential equations driven by multiplicative fractional Gaussian noises in bounded domain where L_t is a…
This paper studies the nonlinear one-dimensional stochastic heat equation driven by a Gaussian noise which is white in time and which has the covariance of a fractional Brownian motion with Hurst parameter 1/4\textless{}H\textless{}1/2 in…
In this article, we consider the stochastic wave and heat equations driven by a Gaussian noise which is spatially homogeneous and behaves in time like a fractional Brownian motion with Hurst index $H>1/2$. The solutions of these equations…
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 present a Feynman-Kac formula for the $1$-dimensional stochastic heat equation (SHE) driven by a time-homogeneous Gaussian white noise potential, where the noise is interpreted in the Wick-It\^o-Skorokhod sense. Our approach consists in…
In this article, we give some existence and smoothness results for the law of the solution to a stochastic heat equation driven by a finite dimensional fractional Brownian motion with Hurst parameter $H>1/2$. Our results rely on recent…
This paper investigates the probability distribution of solutions to McKean--Vlasov stochastic differential equations driven by fractional Brownian motion with Hurst parameter H>1/2. Our main contribution is the derivation of the associated…
The aim of this paper is to study the $d$-dimensional stochastic heat equation with a multiplicative Gaussian noise which is white in space and it has the covariance of a fractional Brownian motion with Hurst parameter $% H\in (0,1)$ in…
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…
The Feynman-Kac equations are a type of partial differential equations describing the distribution of functionals of diffusive motion. The probability density function (PDF) of Brownian functionals satisfies the Feynman-Kac formula, being a…
In this paper, we study the stochastic partial differential equation with multiplicative noise $\frac{\partial u}{\partial t} =\mathcal L u+u\dot W$, where $\mathcal L$ is the generator of a symmetric L\'evy process $X$ and $\dot W$ is a…
The classical Feynman-Kac identity represents solutions of linear partial differential equations in terms of stochastic differential euqations. This representation has been generalized to nonlinear partial differential equations on the one…
We consider the linear stochastic heat equation on $\mathbb{R}^\ell$, driven by a Gaussian noise which is colored in time and space. The spatial covariance satisfies general assumptions and includes examples such as the Riesz kernel in any…
The classical Feynman-Kac formula states the connection between linear parabolic partial differential equations (PDEs), like the heat equation, and expectation of stochastic processes driven by Brownian motion. It gives then a method for…
We establish a probabilistic representation for a wide class of linear deterministic p.d.e.s with potential term, including the wave equation in spatial dimensions 1 to 3. Our representation applies to the heat equation, where it is related…
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…
For the fractional heat equation $\frac{\partial}{\partial t} u(t,x) = -(-\Delta)^{\frac{\alpha}{2}}u(t,x)+ u(t,x)\dot W(t,x)$ where the covariance function of the Gaussian noise $\dot W$ is defined by the heat kernel, we establish…