On square-root boundaries for Bessel processes, and pole-seeking Brownian motion

  • Marc Yor
Conference paper
Part of the Lecture Notes in Mathematics book series (LNM, volume 1095)


Brownian Motion Stochastic Integral Bessel Process Optimal Constant Strong Markov Property 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    M. ABRAMOVITZ, I. STEGUN: Handbook of Mathematical Functions. New-York-Dover-1970.Google Scholar
  2. [2]
    M.T. BARLOW, S.D. JACKA, M. YOR: Inequalities for a couple of processes stopped at an arbitrary random time. To appear (1983).Google Scholar
  3. [3]
    B. DAVIS: On the Lp norms of stochastic integrals and other martingales. Duke Math. Journal, vol. 43, no 4, 697–704 (1976).CrossRefzbMATHGoogle Scholar
  4. [4]
    P. HARTMAN: Uniqueness of principal values, complete monotonicity of logarithmic derivatives of principal solutions and oscillation theorems. Math. Ann. 241, 257–281 (1979).MathSciNetCrossRefzbMATHGoogle Scholar
  5. [5]
    D. KENDALL: Pole-seeking Brownian Motion and Bird Navigation. Journal of the Royal Statistical Society. Series B, 36, no 3, p. 365–417, 1974.MathSciNetzbMATHGoogle Scholar
  6. [6]
    J. KENT: Some probabilistic properties of Bessel functions. Ann. Prob. 6, 760–770 (1978).MathSciNetCrossRefzbMATHGoogle Scholar
  7. [7]
    J. PITMAN, M. YOR: Bessel processes and Infinitely divisible laws. In: "Stochastic Integrals". Lecture Notes in Maths 851. Springer (1981) (ed. D. Williams).Google Scholar
  8. [8]
    L. SHEPP: A first passage problem for the Wiener process. Ann. Math. Stat. 38 (1967), p. 1912–1914.MathSciNetCrossRefzbMATHGoogle Scholar
  9. [9]
    T. SHIGA, S. WATANABE: Bessel diffusions as a one-parameter family of diffusion processes. Z.f.W, 27 (1973), 37–46.MathSciNetCrossRefzbMATHGoogle Scholar
  10. [10]
    S. WATANABE: On Time Inversion of One-Dimensional Diffusion processes. Zeitschrift für Wahr. 31 (1975), 115–124.MathSciNetCrossRefzbMATHGoogle Scholar
  11. [11]
    G.N. WATSON: A treatise on the theory of Bessel functions. Second edition. Cambridge University Press (1966).Google Scholar
  12. [12]
    D. WILLIAMS: Path-decomposition and continuity of local time for one-dimensional diffusions, I Proc. London Math. Soc., Ser. 3, 28, 738–768 (1974).MathSciNetCrossRefzbMATHGoogle Scholar
  13. [13]
    M. YOR: Loi de l'indice du lacet Brownien, et distribution de Hartman-Watson. Z.f.W., 53, 71–95 (1980).MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag 1984

Authors and Affiliations

  • Marc Yor
    • 1
  1. 1.Laboratoire de ProbabilitésUniversité P. et M. CurieParis Cedex 05

Personalised recommendations