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

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.

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

A Note on a Fenyman-kac-type Formula

In this article, we establish a probabilistic representation for the second-order moment of the solution of stochastic heat equation in [0,1]×R , with multiplicative noise, which is fractional in time and colored in space. This representation is similar to the one given in [8] in the case of an s.p.d.e. driven by a Gaussian noise, which is white in time. Unlike the formula of [8], which is base...

Modeling Diffusion to Thermal Wave Heat Propagation by Using Fractional Heat Conduction Constitutive Model

Based on the recently introduced fractional Taylor’s formula, a fractional heat conduction constitutive equation is formulated by expanding the single-phase lag model using the fractional Taylor’s formula. Combining with the energy balance equation, the derived fractional heat conduction equation has been shown to be capable of modeling diffusion-to-Thermal wave behavior of heat propagation by ...

Fractional Feynman-Kac equation for non-brownian functionals.

We derive backward and forward fractional Feynman-Kac equations for the distribution of functionals of the path of a particle undergoing anomalous diffusion. Fractional substantial derivatives introduced by Friedrich and co-workers [Phys. Rev. Lett. 96, 230601 (2006)10.1103/PhysRevLett.96.230601] provide the correct fractional framework for the problem. For applications, we calculate the distri...