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 two of the rough infinite-dimensional systems introduced in \cite{DGT}. The approach combines rough paths methods with standard considerations on discretizing the solutions of stochastic partial differential equations. Explicit rates of convergence are exhibited in case the perturbation is driven by a multidimensional fractional Brownian motion with Hurst index $H>1/3$, and some results of simulation are provided.

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-00460666v1⟩