Variations sur une formule de Paul Lévy

Ph. Biane; M. Yor

Annales de l'I.H.P. Probabilités et statistiques (1987)

  • Volume: 23, Issue: S2, page 359-377
  • ISSN: 0246-0203

How to cite


Biane, Ph., and Yor, M.. "Variations sur une formule de Paul Lévy." Annales de l'I.H.P. Probabilités et statistiques 23.S2 (1987): 359-377. <>.

author = {Biane, Ph., Yor, M.},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {complex Brownian motion; Lévy’s stochastic area; Lévy’s formula; Bessel function; local time},
language = {fre},
number = {S2},
pages = {359-377},
publisher = {Gauthier-Villars},
title = {Variations sur une formule de Paul Lévy},
url = {},
volume = {23},
year = {1987},

AU - Biane, Ph.
AU - Yor, M.
TI - Variations sur une formule de Paul Lévy
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 1987
PB - Gauthier-Villars
VL - 23
IS - S2
SP - 359
EP - 377
LA - fre
KW - complex Brownian motion; Lévy’s stochastic area; Lévy’s formula; Bessel function; local time
UR -
ER -


  1. [1] N.I. Akhiezer, The Classical Moment Problem and Some Related Questions in Analysis, Oliver & Boyd, Edinburgh, 1965. Zbl0135.33803
  2. [2] (a) J.M. Bismut, The Atiyah-Singer Theorems, I et II, Journal Funct. Anal., vol. 57, 1984, p. 56-99 et 329-348. (b) J.M. Bismut, Probability and Geometry. In Probability and Analysis, G. LETTA et M. PRATELLI éd., Lect. Notes in Maths, n° 1206, Springer, 1986. Zbl0538.58033
  3. [3] M. Chaleyat-Maurel et Th. Jeulin, Grossissement gaussien de la filtration brownienne. In Grossissements de filtrations : exemples et applications, Th. JEULIN et M. YOR éd., Lect. Notes in Maths, n° 1118, p. 59-109, Springer, 1985. Zbl0575.60046MR884713
  4. [4] B. Gaveau, Principe de moindre action, propagation de la chaleur et estimées sous-elliptiques sur certains groupes nilpotents, Acta. Math., vol. 139, 1977, p. 96-153. Zbl0366.22010MR461589
  5. [5] J.F. Le Gall, Sur la mesure de Hausdorff de la courbe brownienne, Sém. de Probas. XIX, Lect. Notes in Maths, n° 1123, Springer, 1985. Zbl0563.60071MR889491
  6. [6] P. Levy, Wiener's Random Function, and Other Laplacian Random Functions, Proc. 2nd Berkeley Symp. Math. Stat. Proba., vol. II, 1950, p. 171-186, Univ. California. Zbl0044.13802MR44774
  7. [7] J.W. Pitman et M. Yor, Bessel Processes and Infinitely Divisible Laws, In Stochastic Integrals, D. WILLIAMS éd., Lect. Notes in Maths, n° 851, Springer, 1981. Zbl0469.60076MR620995
  8. [8] G. Szegö, Orthogonal Polynomials, Colloquium Publ., vol. 23, édition révisée, Amer. Math. Soc., Providence, 1959. Zbl0089.27501MR106295
  9. [9] D. Williams, On a Stopped Brownian Motion Formula of H. M. Taylor, Sém. Probas. X, Lect. Notes in Maths, n° 511, Springer, 1976. Zbl0368.60056MR461687
  10. [10] D. Williams, Path Decomposition and Continuity of Local Time for One-Dimensional Diffusion, Proc. London Math. Soc. Ser.3, vol. 28, 1974, p. 738-768. Zbl0326.60093MR350881
  11. [11] D. Williams, Diffusions, Markov Processes and Martingales, vol. I, Foundations, Wiley, 1979. Zbl0402.60003MR531031
  12. [12] M. Yor, Remarques sur une formule de P. Lévy, Sém. de Probas XIV, Lect. Notes in Maths, n° 784, Springer, 1980. Zbl0429.60045MR580140
  13. [13] G.N. Watson, A Treatise on the Theory of Bessel Functions, Cambridge University Press, Second Edition, 1966. Zbl0174.36202MR10746
  14. [14] P. Krée, A Remark on Paul Lévy's Stochastic Area Formula. In Aspect of Mathematics and its Applications, J. A. BARROSO éd., Elsevier Science Publishers, B. V., 1986. Zbl0591.60013

Citations in EuDML Documents

  1. C. Donati-Martin, M. Yor, Fubini's theorem for double Wiener integrals and the variance of the brownian path
  2. Alain Comtet, Yves Tourigny, Excursions of diffusion processes and continued fractions
  3. Patie Pierre, Infinite divisibility of solutions to some self-similar integro-differential equations and exponential functionals of Lévy processes
  4. Laure Coutin, Nicolas Victoir, Enhanced Gaussian processes and applications
  5. Marc Yor, Une explication du théorème de Ciesielski-Taylor

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