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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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A combinatorial method for calculating the moments of Lévy area
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by Daniel Levin and Mark Wildon PDF
Trans. Amer. Math. Soc. 360 (2008), 6695-6709 Request permission

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
  • 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
  • © Copyright 2008 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 360 (2008), 6695-6709
  • MSC (2000): Primary 60J65; Secondary 05A15
  • DOI: https://doi.org/10.1090/S0002-9947-08-04526-1
  • MathSciNet review: 2434307