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Stratonovich's signatures of Brownian motion determine Brownian sample paths

Abstract:
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.

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Publisher copy:
10.1007/s00440-012-0454-z

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Institution:
University of Oxford
Division:
MPLS
Department:
Mathematical Institute
Role:
Author
Journal:
Probability Theory and Related Fields
Volume:
157
Issue:
1-2
Pages:
1-15
Publication date:
2012-01-01
DOI:
EISSN:
1432-2064
ISSN:
0178-8051
Source identifiers:
311147
Pubs id:
pubs:311147
UUID:
uuid:1b2296f6-5115-4b78-a071-d63b7f44518c
Local pid:
pubs:311147
Deposit date:
2013-11-17

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