Skip to Main Content

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.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


Enlacements du mouvement brownien autour des courbes de l’espace
HTML articles powered by AMS MathViewer

by Jean-François Le Gall and Marc Yor PDF
Trans. Amer. Math. Soc. 317 (1990), 687-722 Request permission


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.
  • Lester E. Dubins and Gideon Schwarz, On continuous martingales, Proc. Nat. Acad. Sci. U.S.A. 53 (1965), 913–916. MR 178499, DOI 10.1073/pnas.53.5.913
  • Richard Durrett, A new proof of Spitzer’s result on the winding of two-dimensional Brownian motion, Ann. Probab. 10 (1982), no. 1, 244–246. MR 637391
  • —, Brownian motion and martingales in analysis, Wadsworth, Monterey, Calif., 1984.
  • A. Dvoretzky and P. Erdös, Some problems on random walk in space, Proceedings of the Second Berkeley Symposium on Mathematical Statistics and Probability, 1950, University of California Press, Berkeley-Los Angeles, Calif., 1951, pp. 353–367. MR 0047272
  • R. K. Getoor and M. J. Sharpe, Conformal martingales, Invent. Math. 16 (1972), 271–308. MR 305473, DOI 10.1007/BF01425714
  • Kiyosi Itô, Poisson point processes attached to Markov processes, Proceedings of the Sixth Berkeley Symposium on Mathematical Statistics and Probability (Univ. California, Berkeley, Calif., 1970/1971) Univ. California Press, Berkeley, Calif., 1972, pp. 225–239. MR 0402949
  • Th. Jeulin and M. Yor (eds.), Grossissements de filtrations: exemples et applications, Lecture Notes in Mathematics, vol. 1118, Springer-Verlag, Berlin, 1985 (French). Papers from the seminar on stochastic calculus held at the Université de Paris VI, Paris, 1982/1983. MR 884713, DOI 10.1007/BFb0075765
  • T. Jeulin and M. Yor, Sur les distributions de certaines fonctionnelles du mouvement brownien, Seminar on Probability, XV (Univ. Strasbourg, Strasbourg, 1979/1980) Lecture Notes in Math., vol. 850, Springer, Berlin-New York, 1981, pp. 210–226 (French). MR 622565
  • Frank B. Knight, A reduction of continuous square-integrable martingales to Brownian motion, Martingales (Rep. Meeting, Oberwolfach, 1970) Lecture Notes in Math., Vol. 190, Springer, Berlin, 1971, pp. 19–31. MR 0370741
  • Frank B. Knight, On the sojourn times of killed Brownian motion, Séminaire de Probabilités, XII (Univ. Strasbourg, Strasbourg, 1976/1977) Lecture Notes in Math., vol. 649, Springer, Berlin, 1978, pp. 428–445. MR 520018
  • Jean-François Le Gall, Sur les fonctions polaires pour le mouvement brownien, Séminaire de Probabilités, XXII, Lecture Notes in Math., vol. 1321, Springer, Berlin, 1988, pp. 186–189 (French). MR 960526, DOI 10.1007/BFb0084136
  • J.-F. Le Gall and M. Yor, Étude asymptotique de certains mouvements browniens complexes avec drift, Probab. Theory Relat. Fields 71 (1986), no. 2, 183–229 (French). MR 816704, DOI 10.1007/BF00332310
  • Jean-François Le Gall and Marc Yor, Excursions browniennes et carrés de processus de Bessel, C. R. Acad. Sci. Paris Sér. I Math. 303 (1986), no. 3, 73–76 (French, with English summary). MR 851079
  • —, Sur certaines lois limites intervenant dans l’étude des enlacements du mouvement brow nien dans ${{\mathbf {R}}^3}$ (en préparation).
  • J.-F. Le Gall and M. Yor, Étude asymptotique des enlacements du mouvement brownien autour des droites de l’espace, Probab. Theory Related Fields 74 (1987), no. 4, 617–635 (French, with English summary). MR 876259, DOI 10.1007/BF00363519
  • P. Messulam and M. Yor, On D. Williams’ “pinching method” and some applications, J. London Math. Soc. (2) 26 (1982), no. 2, 348–364. MR 675178, DOI 10.1112/jlms/s2-26.2.348
  • Jim Pitman and Marc Yor, A decomposition of Bessel bridges, Z. Wahrsch. Verw. Gebiete 59 (1982), no. 4, 425–457. MR 656509, DOI 10.1007/BF00532802
  • Jim Pitman and Marc Yor, Asymptotic laws of planar Brownian motion, Ann. Probab. 14 (1986), no. 3, 733–779. MR 841582
  • Frank Spitzer, Some theorems concerning $2$-dimensional Brownian motion, Trans. Amer. Math. Soc. 87 (1958), 187–197. MR 104296, DOI 10.1090/S0002-9947-1958-0104296-5
  • D. Williams, A simple geometric proof of Spitzer’s winding number formula for $2$-dimensional Brownian motion, University College, Swansea, unpublished manuscript.
  • David Williams, Diffusions, Markov processes, and martingales. Vol. 1, Probability and Mathematical Statistics, John Wiley & Sons, Ltd., Chichester, 1979. Foundations. MR 531031
  • Marc Yor, Sur quelques approximations d’intégrales stochastiques, Séminaire de Probabilités, XI (Univ. Strasbourg, Strasbourg, 1975/1976) Lecture Notes in Math., Vol. 581, Springer, Berlin, 1977, pp. 518–528 (French). MR 0448556
Similar Articles
  • Retrieve articles in Transactions of the American Mathematical Society with MSC: 60J65
  • Retrieve articles in all journals with MSC: 60J65
Additional Information
  • © Copyright 1990 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 317 (1990), 687-722
  • MSC: Primary 60J65
  • DOI:
  • MathSciNet review: 946219