On Walsh's Brownian motions

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


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  1. [BwPY1]
    Barlow, M.T., Pitman, J.W. and Yor, M. (1989). Une extension multidimensionelle de la loi de l'arc sinus. In this volume.Google Scholar
  2. [BwPY2]
    Barlow, M.T., Pitman, J.W. and Yor, M. (1989). Some extensions of the arcsine law. Tech. Report # 189, Dept. Statistics, U.C. Berkeley.Google Scholar
  3. [BC]
    Baxter, J.R. and Chacon, R.V. (1984). The equivalence of diffusions on networks to Brownian motion. Contemp. Math. 26, 33–47.MathSciNetCrossRefzbMATHGoogle Scholar
  4. [ByPY]
    Burdzy, K., Pitman, J.W. and Yor, M. (1989). Some asymptotic laws for crossings and excursions. Colloque Paul Lévy sur les Processus Stochastiques, Astérisque 157–158, 59–74.MathSciNetzbMATHGoogle Scholar
  5. [DV]
    Davis, M.H.A. and Varaiya, P. (1974). The multiplicity of an increasing family of σ-fields. Ann. Prob. 2, 958–963.MathSciNetCrossRefzbMATHGoogle Scholar
  6. [E]
    El Karoui, N. A propos de la formule d'Azéma-Yor. Sém. Prob. XIII. Lecture Notes in Math. 721, Springer, 443–452.Google Scholar
  7. [FD]
    Frank, H.F. and Durham, S. (1984). Random motion on binary trees. J. Appl. Prob. 21 58–69.MathSciNetCrossRefzbMATHGoogle Scholar
  8. [HS]
    Harrison, J.M. and Shepp, L.A. (1981). On skew Brownian motion. Ann. Prob. 9, 309–313.MathSciNetCrossRefzbMATHGoogle Scholar
  9. [I]
    Itô, K. (1970): Poisson point processes attached to Markov processes. Proc. Sixth Berkeley Symp. Math. Statist. Prob. University of California Press, Berkeley, pp. 225–239.Google Scholar
  10. [J]
    Jacod, J. (1976). A general theorem of representation for martingales. Z. Wahrscheinlichkeitstheorie verw. Gebeite 34, 225–244.MathSciNetCrossRefzbMATHGoogle Scholar
  11. [Je]
    Jeulin, T. (1980). Semi-Martingales et Grossissement d'une Filtration. Lecture Notes in Math. 833, Springer-Verlag.Google Scholar
  12. [L]
    LeGall, J-F (1983). Applications du temps local aux équations différentielles stochastiques unidimensionelles. Sém. Prob. XVII. Lecture Notes in Math. 986, Springer-Verlag, 15–31.MathSciNetCrossRefGoogle Scholar
  13. [LY]
    Le Gall J.F. and Yor M. (1986). Etude asymptotique de certains mouvements browniens avec drift. Probability and Related Fields, 71, 183–229MathSciNetCrossRefzbMATHGoogle Scholar
  14. [LR]
    Lindvall, T. and Rogers, L.C.G. (1986). Coupling of multidimensional diffusions by reflection. Ann. Prob. 14, 860–872.MathSciNetCrossRefzbMATHGoogle Scholar
  15. [MSY]
    Meyer, P.A., Stricker, C. and Yor, M. (1979). Sur une formule de la théorie du balayage. Sém. Prob. XIII. Lecture Notes in Math. 721, Springer-Verlag, 478–487.MathSciNetCrossRefzbMATHGoogle Scholar
  16. [M]
    Millar, P.W. (1977). Germ sigma fields and the natural state space of a Markov process. Z. Wahrscheinlichkeitstheorie verw. Gebeite 39, 85–101.MathSciNetCrossRefzbMATHGoogle Scholar
  17. [N]
    Nakao, S. (1972). On the pathwise uniqueness of solutions of stochastic differential equations. Osaka J. Math. 9, 513–518.MathSciNetzbMATHGoogle Scholar
  18. [PY]
    Pitman, J. and Yor, M. (1986a). Asymptotic laws of planar Brownian motion. Ann. Prob. 14, 733–779.MathSciNetCrossRefzbMATHGoogle Scholar
  19. [R]
    Rogers, L.C.G. (1983). Itô excursion theory via resolvents. Z. Wahrscheinlichkeitstheorie verw. Gebeite 63, 237–255.CrossRefzbMATHGoogle Scholar
  20. [S]
    Salisbury, T.S. (1986). Construction of right processes from excursions. Z. Wahrscheinlichkeitstheorie verw. Gebeite 73, 351–367.MathSciNetzbMATHGoogle Scholar
  21. [Sk]
    Skorokhod, A. V. (1987). Random processes in infinite dimensional spaces (in Russian). Proceedings of the International Congress of Mathematicians: August 3–11, 1986, Berkeley [edited by Andrew M. Gleason]. American Mathematical Society, Providence, R.I., 163–171.Google Scholar
  22. [St]
    Stricker, C. (1981). Sur un théorème de H. J. Engelbert et J. Hess. Stochastics 6, 73–77.MathSciNetCrossRefzbMATHGoogle Scholar
  23. [SY]
    Stroock, D.W. and Yor, M. (1980). On extremal solutions of martingale problems. Ann. Scient. E.N.S., 4ième série, 13, 95–164.MathSciNetzbMATHGoogle Scholar
  24. [V]
    Varopoulos, N. Th. (1985). Long range estimates for Markov Chains. Bull. Sci. Math. 109, 225–252.MathSciNetzbMATHGoogle Scholar
  25. [VW]
    Van der Weide, J.A.M. (1987). Stochastic processes and point processes of excursions. Ph.D. Thesis, Technische Universiteit Delft.Google Scholar
  26. [W]
    Walsh, J. (1978). A diffusion with a discontinuous local time. In: Temps Locaux, Astérisque 52–53, 37–45.Google Scholar
  27. [Wei]
    Weizsäcker, H.v. (1983). Exchanging the order of taking suprema and countable intersection of sigma algebras. Ann. Inst. H. Poincaré 19, 91–100.zbMATHGoogle Scholar
  28. [Y0]
    Yor, M. (1978). Sous-espaces denses dans L 1 ou H 1 et représentation des martingales, Sém. Prob. XII, Lecture Notes in Math. 649, Springer, 265–309.CrossRefzbMATHGoogle Scholar
  29. [Y1]
    Yor, M. (1979). Sur le balayage des semi-martingales continues. Sém. Prob. XIII. Lecture Notes in Math. 721, Springer-Verlag, 453–171.MathSciNetCrossRefzbMATHGoogle Scholar
  30. [Y2]
    Yor, M. (1979). Sur les martingales continues extrémales. Stochastics 2, 191–196.MathSciNetCrossRefzbMATHGoogle 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.Laboratorie de ProbabilitésUniversité Pierre et Marie CurieParis Cedex 05France

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