On the law of the solution to a stochastic heat equation with fractional noise in time

Solesne Bourguin (1) , Ciprian A. Tudor (2)

1 SAMM - Statistique, Analyse et Modélisation Multidisciplinaire (SAmos-Marin Mersenne)
2 LPP - Laboratoire Paul Painlevé - UMR 8524

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 bifractional Brownian motion.

Mots clés: Stochastic heat equation; Gaussian noise; bifractional Brownian motion

Domaines: Probabilités [math.PR]

Solesne Bourguin, Ciprian A. Tudor. On the law of the solution to a stochastic heat equation with fractional noise in time. 2011. ⟨hal-00631250⟩