Stratonovich's Signatures of Brownian Motion Determine Brownian Sample Paths

2011/02/17 by Yves Lejan, Yves LeJan, Zhongmin Qian +2
Economics, Econometrics and Finance · Mathematics · #FOS: Mathematics #Mathematical Dynamics and Fractals #Probability (math.PR) #Stochastic processes and financial applications #Stochastic processes and statistical mechanics #math.PR

paper · pdf · doi:10.48550/arxiv.1102.3601

arxiv created 2011/02/17 · openalex publication_date 2011/02/17 · arxiv updated 2011/02/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The signature of Brownian motion in 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≥ 2, almost all Brownian motion sample paths (running up to time T) are determined by its signature over [0,T]

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