Stratonovich's signatures of Brownian motion determine Brownian sample paths

Yves Le Jan, Zhongmin Qian

Research output: Contribution to journalArticlepeer-review


The signature of Brownian motion in ℝd 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 their signature over [0,T].

Original languageEnglish (US)
Pages (from-to)209-223
Number of pages15
JournalProbability Theory and Related Fields
Issue number1-2
StatePublished - Oct 2013


  • Brownian motion
  • Rough paths
  • Signatures

ASJC Scopus subject areas

  • Analysis
  • Statistics and Probability
  • Statistics, Probability and Uncertainty


Dive into the research topics of 'Stratonovich's signatures of Brownian motion determine Brownian sample paths'. Together they form a unique fingerprint.

Cite this