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The signature of Brownian motion in {Mathematical expression} over a running time interval {Mathematical expression} is the collection of all iterated Stratonovich path integrals along the Brownian motion. We show that, in dimension {Mathematical expression}, almost all Brownian motion sample paths (running up to time {Mathematical expression}) are determined by their signature over {Mathematical expression}. © 2012 Springer-Verlag Berlin Heidelberg

Stratonovich’s signatures of Brownian motion determine Brownian sample paths