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

TL;DR
This paper extends Donsker's invariance principle to rough path topology, enabling new weak limit theorems for stochastic integrals and differential equations driven by random walks.
Contribution
It introduces a novel application of rough path theory to Donsker's invariance principle, broadening its scope to stochastic calculus.
Findings
Donsker's invariance principle holds in rough path topology.
Established weak limit theorems for stochastic integrals.
Extended invariance principles to differential equations driven by random walks.
Abstract
Donsker's invariance principle is shown to hold for random walks in rough path topology. As application, we obtain Donsker-type weak limit theorems for stochastic integrals and differential equations.
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Taxonomy
TopicsMathematical Dynamics and Fractals · Stochastic processes and financial applications · Stochastic processes and statistical mechanics
