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A combinatorial method for calculating the moments of Lévy area
Author(s):
Daniel
Levin;
Mark
Wildon
Journal:
Trans. Amer. Math. Soc.
360
(2008),
6695-6709.
MSC (2000):
Primary 60J65;
Secondary 05A15
Posted:
July 24, 2008
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Abstract:
We present a new way to compute the moments of the Lévy area of a two-dimensional Brownian motion. Our approach uses iterated integrals and combinatorial arguments involving the shuffle product.
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Additional Information:
Daniel
Levin
Affiliation:
Mathematical Institute, University of Oxford, 24-29 St Giles’, Oxford OX1 3LB, United Kingdom
Email:
levin@maths.ox.ac.uk
Mark
Wildon
Affiliation:
Department of Mathematics, University of Wales, Swansea, Singleton Park, Swansea SA2 8PP, United Kingdom
Email:
m.j.wildon@swansea.ac.uk
DOI:
10.1090/S0002-9947-08-04526-1
PII:
S 0002-9947(08)04526-1
Keywords:
L\'evy area,
shuffle product,
signature of a path
Received by editor(s):
February 1, 2007
Received by editor(s) in revised form:
April 16, 2007
Posted:
July 24, 2008
Additional Notes:
The first author was supported by the EPSRC Fellowship ‘‘Partial differential equations - A rough path approach” GR/S18526/01
The second author was supported by EPSRC Grant EP/D054664/1
Copyright of article:
Copyright
2008,
American Mathematical Society
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