Stratonovich's Signatures of Brownian Motion Determine Brownian Sample Paths

Details Stratonovich's Signatures of Brownian Motion Determine Brownian Sample Paths Stratonovich's Signatures of Brownian Motion Determine Brownian Sample Paths

2011-02-17

arxiv.org/abs/1102.3601v1

Mathematics

Probability

Scientific paper

The signature of Brownian motion in $\mathbb{R}^{d}$ over a running time
interval $[0,T]$ is the collection of all iterated Stratonovich path integrals
along the Brownian motion. We show that, in dimension $d\geq 2$, almost all
Brownian motion sample paths (running up to time $T$) are determined by its
signature over $[0,T]$

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