Stratonovich's signatures of Brownian motion determine Brownian sample paths

Yves Le Jan; Zhongmin Qian

doi:10.1007/s00440-012-0454-z

Stratonovich's signatures of Brownian motion determine Brownian sample paths

Yves Le Jan, Zhongmin Qian

Mathematics

Research output: Contribution to journal › Article › peer-review

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 their signature over [0,T].

Original language	English (US)
Pages (from-to)	209-223
Number of pages	15
Journal	Probability Theory and Related Fields
Volume	157
Issue number	1-2
DOIs	https://doi.org/10.1007/s00440-012-0454-z
State	Published - Oct 2013

Keywords

Brownian motion
Rough paths
Signatures

ASJC Scopus subject areas

Analysis
Statistics and Probability
Statistics, Probability and Uncertainty

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10.1007/s00440-012-0454-z

Cite this

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title = "Stratonovich's signatures of Brownian motion determine Brownian sample paths",

abstract = "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].",

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author = "{Le Jan}, Yves and Zhongmin Qian",

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doi = "10.1007/s00440-012-0454-z",

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AB - 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].

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KW - Rough paths

KW - Signatures

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ER -

Stratonovich's signatures of Brownian motion determine Brownian sample paths

Abstract

Keywords

ASJC Scopus subject areas

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