Research supported in part by National Science Foundation Grant DMS88-01808
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Barlow, M.T., Pitman, J.W. and Yor, M. (1989). Une extension multidimensionelle de la loi de l'arc sinus. In this volume.
Barlow, M.T., Pitman, J.W. and Yor, M. (1989). Some extensions of the arcsine law. Tech. Report # 189, Dept. Statistics, U.C. Berkeley.
Baxter, J.R. and Chacon, R.V. (1984). The equivalence of diffusions on networks to Brownian motion. Contemp. Math. 26, 33–47.
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.
Davis, M.H.A. and Varaiya, P. (1974). The multiplicity of an increasing family of σ-fields. Ann. Prob. 2, 958–963.
El Karoui, N. A propos de la formule d'Azéma-Yor. Sém. Prob. XIII. Lecture Notes in Math. 721, Springer, 443–452.
Frank, H.F. and Durham, S. (1984). Random motion on binary trees. J. Appl. Prob. 21 58–69.
Harrison, J.M. and Shepp, L.A. (1981). On skew Brownian motion. Ann. Prob. 9, 309–313.
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.
Jacod, J. (1976). A general theorem of representation for martingales. Z. Wahrscheinlichkeitstheorie verw. Gebeite 34, 225–244.
Jeulin, T. (1980). Semi-Martingales et Grossissement d'une Filtration. Lecture Notes in Math. 833, Springer-Verlag.
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.
Le Gall J.F. and Yor M. (1986). Etude asymptotique de certains mouvements browniens avec drift. Probability and Related Fields, 71, 183–229
Lindvall, T. and Rogers, L.C.G. (1986). Coupling of multidimensional diffusions by reflection. Ann. Prob. 14, 860–872.
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.
Millar, P.W. (1977). Germ sigma fields and the natural state space of a Markov process. Z. Wahrscheinlichkeitstheorie verw. Gebeite 39, 85–101.
Nakao, S. (1972). On the pathwise uniqueness of solutions of stochastic differential equations. Osaka J. Math. 9, 513–518.
Pitman, J. and Yor, M. (1986a). Asymptotic laws of planar Brownian motion. Ann. Prob. 14, 733–779.
Rogers, L.C.G. (1983). Itô excursion theory via resolvents. Z. Wahrscheinlichkeitstheorie verw. Gebeite 63, 237–255.
Salisbury, T.S. (1986). Construction of right processes from excursions. Z. Wahrscheinlichkeitstheorie verw. Gebeite 73, 351–367.
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.
Stricker, C. (1981). Sur un théorème de H. J. Engelbert et J. Hess. Stochastics 6, 73–77.
Stroock, D.W. and Yor, M. (1980). On extremal solutions of martingale problems. Ann. Scient. E.N.S., 4ième série, 13, 95–164.
Varopoulos, N. Th. (1985). Long range estimates for Markov Chains. Bull. Sci. Math. 109, 225–252.
Van der Weide, J.A.M. (1987). Stochastic processes and point processes of excursions. Ph.D. Thesis, Technische Universiteit Delft.
Walsh, J. (1978). A diffusion with a discontinuous local time. In: Temps Locaux, Astérisque 52–53, 37–45.
Weizsäcker, H.v. (1983). Exchanging the order of taking suprema and countable intersection of sigma algebras. Ann. Inst. H. Poincaré 19, 91–100.
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.
Yor, M. (1979). Sur le balayage des semi-martingales continues. Sém. Prob. XIII. Lecture Notes in Math. 721, Springer-Verlag, 453–171.
Yor, M. (1979). Sur les martingales continues extrémales. Stochastics 2, 191–196.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1989 Springer-Verlag
About this paper
Cite this paper
Barlow, M., Pitman, J., Yor, M. (1989). On Walsh's Brownian motions. In: Azéma, J., Yor, M., Meyer, P.A. (eds) Séminaire de Probabilités XXIII. Lecture Notes in Mathematics, vol 1372. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0083979
Download citation
DOI: https://doi.org/10.1007/BFb0083979
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-51191-5
Online ISBN: 978-3-540-46176-0
eBook Packages: Springer Book Archive