Numerical schemes for the rough heat equation

Aurélien Deya (1)

1 IECN - Institut Élie Cartan de Nancy

This paper is devoted to the study of numerical approximation schemes for the heat equation on $(0,1)$ perturbed by a non-linear rough signal. It is the continuation of \cite{RHE,RHE-glo}, where the existence and uniqueness of a solution has been established. The approach combines rough paths methods with standard considerations on discretizing stochastic PDEs. The results apply to a geometric $2$-rough path, which covers the case of the multidimensional fractional Brownian motion with Hurst index $H>1/3$.

Mots clés: Rough paths theory; Stochastic PDEs; Approximation schemes; Fractional Brownian motion

Domaines: Probabilités [math.PR]

Aurélien Deya. Numerical schemes for the rough heat equation. 2010. ⟨hal-00460666v2⟩