From random walks to rough paths

Breuillard, Emmanuel; Friz, Peter; Huesmann, Martin

doi:10.1090/S0002-9939-09-09930-4

From random walks to rough paths
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by Emmanuel Breuillard, Peter Friz and Martin Huesmann PDF

Proc. Amer. Math. Soc. 137 (2009), 3487-3496 Request permission

Abstract:

Donsker’s invariance principle is shown to hold for random walks in rough path topology. As an application, we obtain Donsker-type weak limit theorems for stochastic integrals and differential equations.

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