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A combinatorial method for calculating the moments of Lévy area

Authors: Daniel Levin and Mark Wildon
Journal: Trans. Amer. Math. Soc. 360 (2008), 6695-6709
MSC (2000): Primary 60J65; Secondary 05A15
Published electronically: July 24, 2008
MathSciNet review: 2434307
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Abstract | References | Similar Articles | Additional Information

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

Mark Wildon
Affiliation: Department of Mathematics, University of Wales, Swansea, Singleton Park, Swansea SA2 8PP, United Kingdom

Keywords: Lévy area, shuffle product, signature of a path
Received by editor(s): February 1, 2007
Received by editor(s) in revised form: April 16, 2007
Published electronically: 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
Article copyright: © Copyright 2008 American Mathematical Society