Renewal property of the extrema and tree property of the excursion of a one-dimensional brownian motion

  • J. Neveu
  • J. Pitman
Conference paper
Part of the Lecture Notes in Mathematics book series (LNM, volume 1372)


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  1. [B]
    Brox, Th. (1986). One dimensional diffusion processes in a Wiener medium. Ann. Proba. 14, 1206–1218.MathSciNetCrossRefzbMATHGoogle Scholar
  2. [K]
    Kesten, H. (1986). The limit distribution of Sinaï's walk in random environment. Physica 138A, 299–309.MathSciNetCrossRefzbMATHGoogle Scholar
  3. [M]
    Maisonneuve, B. (1975). Exit systems. Ann. Proba. 3, 399–411.MathSciNetCrossRefzbMATHGoogle Scholar
  4. [N1]
    Neveu, J. (1977). Processu ponctuels in Ecole d'Eté de Probabilités de St Flour VI-1976, Lect. Notes in Math. 598, 249–447, Springer.MathSciNetCrossRefGoogle Scholar
  5. [N2]
    Neveu, J. (1986). Erasing a branching tree. Supplement to Adv. Applied Proba., Papers in honour of G.E.H. Reuter, 101–108.Google Scholar
  6. [NP*]
    Neveu, J. and Pitman, J. The branching process in a Brownian motion excursion. This volume.Google Scholar
  7. [S]
    Sinaï, Y.G. (1982). The limiting behavior of a one-dimensional random walk in a random medium. Theory Proba. Appl. 27, 256–268.CrossRefGoogle Scholar
  8. [T]
    Tanaka, H. (1987). Limit theorem for one dimensional diffusion process in Brownian environment. Stochastic Analysis, Proc. Paris 1987, Ed. Metivier-Watanabe. Lect. Notes in Math. 1322, Springer, pp. 156–172.Google Scholar
  9. [W]
    Walsh, J. (1978). Downcrossings and the Markov property of local time. In: Temps locaux. Astérisque 52–53, 89–115. Soc. Math. France.Google Scholar

Copyright information

© Springer-Verlag 1989

Authors and Affiliations

  • J. Neveu
    • 1
  • J. Pitman
    • 2
  1. 1.Laboratoire de ProbabilitésUniversité P. et M. CurieParis Cedex 05
  2. 2.Department of StatisticsUniversity of CaliforniaBerkeleyUnited States

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