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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles 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 1.48.

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Enlacements du mouvement brownien autour des courbes de l’espace
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by Jean-François Le Gall and Marc Yor PDF
Trans. Amer. Math. Soc. 317 (1990), 687-722 Request permission

Abstract:

Limit theorems are proved for the winding numbers of a three-dimensional Brownian motion around certain curves in space. In particular, the joint asymptotic distribution of the winding numbers around two curves is obtained. This joint distribution generalizes the asymptotic law of the winding numbers of a planar Brownian motion around two points, which has recently been given by Pitman and Yor. The limiting distributions are closely related to the time spent by a linear Brownian motion above and below a multiple of its maximum process. Proofs rely on stochastic calculus for continuous semi-martingales.
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Additional Information
  • © Copyright 1990 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 317 (1990), 687-722
  • MSC: Primary 60J65
  • DOI: https://doi.org/10.1090/S0002-9947-1990-0946219-0
  • MathSciNet review: 946219