Numerical Schemes for Rough Parabolic Equations

Aurélien Deya (1)

1 IECN - Institut Élie Cartan de Nancy

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 > 1/3.

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

Domaines: Probabilités [math.PR]

Aurélien Deya. Numerical Schemes for Rough Parabolic Equations. Applied Mathematics and Optimization, 2012, ⟨10.1007/s00245-011-9157-6⟩. ⟨hal-00460666v3⟩