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A multiscale guide to Brownian motion

Abstract:

We revise the Levy's construction of Brownian motion as a simple though rigorous approach to operate with various Gaussian processes. A Brownian path is explicitly constructed as a linear combination of wavelet-based ``geometrical features'' at multiple length scales with random weights. Such a wavelet representation gives a closed formula mapping of the unit interval onto the functional space of Brownian paths. This formula elucidates many classical results about Brownian motion (e.g., non...

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Publication status:
Accepted
Peer review status:
Peer reviewed

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Institution:
University of Oxford
Division:
MPLS
Department:
Mathematical Institute
Role:
Author
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Funding agency for:
Belyaev, D
Grant:
EP/M002896/1
Publisher:
Institute of Physics Publisher's website
Journal:
Journal of Physics A: Mathematical and Theoretical Journal website
Publication date:
2015-01-01
ISSN:
1751-8121
Source identifiers:
573427
Keywords:
Pubs id:
pubs:573427
UUID:
uuid:7f04e54d-db18-4c87-9728-0328047e5c5d
Local pid:
pubs:573427
Deposit date:
2015-11-16

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