Feynman–Kac formula for heat equation driven by fractional white noise

Feynman-Kac formula for fractional heat equation driven by fractional white noise

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 of symmetric stable Lévy motion. This difficulty will be overcome by a technique developed in the framework of large deviation. This Feynman-Kac formula is ...

Feynman–kac Formula for Heat Equation Driven by Fractional White Noise by Yaozhong Hu, David Nualart

Feynman-Kac formula for heat equation driven by fractional white noise

In this paper we establish a version of the Feynman-Kac formula for the stochastic heat equation with a multiplicative fractional Brownian sheet. We prove the smoothness of the density of the solution, and the Hölder regularity in the space and time variables.

Stochastic Heat Equation Driven by Fractional Noise and Local Time

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 ∈ (0, 1) in time. Two types of equations are considered. First we consider the equation in the Itô-Skorohod sense, and later in the Stratonovich sense. An explicit chaos developm...

A quasilinear stochastic partial differential equation driven by fractional white noise

We approximate the solution of a quasilinear stochastic partial differential equation driven by fractional Brownian motion BH(t); H ∈ (0, 1), which was calculated via fractional White Noise calculus, see [5].