Malliavin calculus for fractional heat equation

Aurélien Deya (1) , Samy Tindel (2, 1)

1 IECL - Institut Élie Cartan de Lorraine
2 BIGS - Biology, genetics and statistics

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.

Keywords: Malliavin calculus; heat equation; fractional Brownian motion

Domains: Probability [math.PR]

Aurélien Deya, Samy Tindel. Malliavin calculus for fractional heat equation. Malliavin Calculus and stochastic analysis : a festschrift in honor of David Nualart, Springer, 583 p., 2013, Springer Proceedings in Mathematics & Statistics, 978-1-4614-5906-4. ⟨hal-00618597v2⟩