Une extension multidimensionnelle de la loi de l'arc sinus

  • Martin Barlow
  • Jim Pitman
  • Marc Yor
Conference paper
Part of the Lecture Notes in Mathematics book series (LNM, volume 1372)

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    J.K. Brooks, R.V. Chacon: Diffusions as a limit of stretched Brownian motions. Adv. in Maths, vol. 49, no 2, 109–122 (1983).MathSciNetCrossRefMATHGoogle Scholar
  2. [2]
    J. Franchi: Produit semi-direct de diffusions réelles et lois asymptotiques. A paraître au Journal of App. Proba. (1989)Google Scholar
  3. [3]
    J.M. Harrison, L.A. Shepp: On skew brownian motion. Ann. Proba. 9, 309–313 (1981).MathSciNetCrossRefMATHGoogle Scholar
  4. [4]
    K. Itô, H.P. Mc Kean: Diffusion processes and their sample paths. Springer (1965).Google Scholar
  5. [5]
    I. Karatzas, S.E. Shreve: Brownian motion and stochastic calculus. Springer (1987).Google Scholar
  6. [6]
    J.F. Le Gall: One-dimensional stochastic differential equations involving the local times of the unknown process. In: Stochastic Analysis and Applications (eds. A. Truman, D. Williams). Lect. Notes in Maths 1095. Springer (1984).Google Scholar
  7. [7]
    J.W. Pitman, M. Yor: Asymptotic laws of planar Brownian motion. Ann. Probas. 14, 733–779 (1986).MathSciNetCrossRefMATHGoogle Scholar
  8. [8]
    L.C.G. Rogers, D. Williams: Diffusions, Markov processes and Martingales. Vol. 2: Itô Calculus. J. Wiley (1987).Google Scholar
  9. [9]
    W. Rosenkrantz: Limit theorems for solutions to a class of stochastic differential equations. Indiana Math. J. 24, 613–625 (1975).MathSciNetCrossRefMATHGoogle Scholar
  10. [10]
    J.B. Walsh: A diffusion with discontinuous local time. Astérisque 52–53, 37–45 (1978).Google Scholar
  11. [11a]
    P. Lévy: Sur un problème de M. Marcinkiewicz. C.R.A.S. 208 (1939), p. 318–321. Errata p. 776.MATHGoogle Scholar
  12. [11b]
    P. Lévy: Sur certains processus stochastiques homogènes. Compositio Math., t. 7, 1939, p. 283–339.MathSciNetMATHGoogle Scholar
  13. [12]
    D. Williams: Markov properties of Brownian local time. Bull. Amer. Math. Soc. 75, 1035–1036 (1969).MathSciNetCrossRefMATHGoogle Scholar
  14. [13]
    M. Kac: On some connections between probability theory and differential and integral equations. Proc. 2nd Berkeley Symp. on Math. Stat. and Probability, 189–215 (1951), University of California Press.Google Scholar
  15. [14]
    M.T. Barlow, J.W. Pitman, M. Yor: On Walsh's Brownian Motions. Dans ce volume.Google Scholar
  16. [15]
    M.T. Barlow, J.W. Pitman, M. Yor: Some extensions of the arc sine law. Technical Report no 189. Department of Statistics, U.C. Berkeley (1989).Google Scholar
  17. [16]
    J. Kent: Some probabilistic properties of Bessel functions. Ann. Prob. 6, 760–770 (1978).MathSciNetCrossRefMATHGoogle Scholar
  18. [17]
    S.A. Molchanov, E. Ostrovski: Symmetric stable processes as traces of degenerate diffusion processes. Theory of Proba. and its App., vol. XIV, no 1, 128–131 (1969).CrossRefMATHGoogle Scholar
  19. [18]
    E.B. Dynkin: Some limit theorems for sums of independent random variables with infinite mathematical expectations. Selected Transl. in Math. Stat. and Probability, vol. 1, 1961, IMS-AMS, p. 171–189 (1961).MathSciNetMATHGoogle Scholar

Copyright information

© Springer-Verlag 1989

Authors and Affiliations

  • Martin Barlow
    • 1
  • Jim Pitman
    • 2
  • Marc Yor
    • 3
  1. 1.Trinity CollegeCambridgeEngland
  2. 2.Department of StatisticsUniversity of CaliforniaBerkeleyUnited States
  3. 3.Laboratoire de ProbabilitésUniversité P. et M. CurieParis Cedex 05France

Personalised recommendations