Malliavin calculus for fractional heat equation

TL;DR

This paper investigates the existence and smoothness of the probability law of solutions to a stochastic heat equation driven by fractional Brownian motion with Hurst parameter greater than 1/2, using advanced stochastic analysis and Young integration techniques.

Contribution

It introduces new results on the law's smoothness for fractional heat equations using modern Young integration and stochastic analysis methods.

Findings

Established existence of solutions for the fractional heat equation.

Proved smoothness properties of the solution's law.

Applied Young integration techniques to stochastic convolution integrals.

Abstract

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 tools of Young integration for convolutional integrals combined with stochastic analysis methods for the study of laws of random variables defined on a Wiener space.