Numerical Schemes for Rough Parabolic Equations
arXiv:1003.0587 · doi:10.1007/s00245-011-9157-6
Abstract
This paper is devoted to the study of numerical approximation schemes for a class of parabolic equations on (0, 1) perturbed by a non-linear rough signal. It is the continuation of [8, 7], 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 \textgreater{} 1/3.
Applied Mathematics and Optimization, 2012
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