Numerical schemes for the rough heat equation

Details Numerical schemes for the rough heat equation Numerical schemes for the rough heat equation

2010-03-02

arxiv.org/abs/1003.0587v2

Mathematics

Probability

Scientific paper

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 $H>1/3$.

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