Une extension multidimensionnelle de la loi de l'arc sinus
Séminaire de probabilités de Strasbourg, Volume 23  (1989), p. 294-314
@article{SPS_1989__23__294_0,
     author = {Barlow, Martin T. and Pitman, Jim and Yor, Marc},
     title = {Une extension multidimensionnelle de la loi de l'arc sinus},
     journal = {S\'eminaire de probabilit\'es de Strasbourg},
     publisher = {Springer - Lecture Notes in Mathematics},
     volume = {23},
     year = {1989},
     pages = {294-314},
     zbl = {0738.60072},
     mrnumber = {1022918},
     language = {en},
     url = {http://www.numdam.org/item/SPS_1989__23__294_0}
}
Barlow, Martin T.; Pitman, Jim; Yor, Marc. Une extension multidimensionnelle de la loi de l'arc sinus. Séminaire de probabilités de Strasbourg, Volume 23 (1989) , pp. 294-314. http://www.numdam.org/item/SPS_1989__23__294_0/

[1] J.K. Brooks, R.V. Chacon : Diffusions as a limit of stretched Brownian motions. Adv. in Maths, vol. 49, n° 2, 109-122 (1983). | MR 714586 | Zbl 0542.60079

[2] J. Franchi : Produit semi-direct de diffusions réelles et lois asymptotiques. A paraître au Journal of App. Proba. (1989) | MR 1039626 | Zbl 0694.60073

[3] J.M. Harrison, L.A. Shepp : On skew brownian motion. Ann. Proba. 9, 309-313 (1981). | MR 606993 | Zbl 0462.60076

[4] K. Itô, H.P. Mc Kean : Diffusion processes and their sample paths. Springer (1965). | Zbl 0127.09503

[5] I. Karatzas, S.E. Shreve : Brownian motion and stochastic calculus. Springer (1987). | Zbl 0638.60065

[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). | MR 777514 | Zbl 0551.60059

[7] J.W. Pitman, M. Yor : Asymptotic laws of planar Brownian motion. Ann. Probas. 14, 733-779 (1986). | MR 841582 | Zbl 0607.60070

[8] L.C.G. Rogers, D. Williams : Diffusions, Markov processes and Martingales. Vol. 2 : Itô Calculus. J. Wiley (1987). | MR 921238 | Zbl 0627.60001

[9] W. Rosenkrantz : Limit theorems for solutions to a class of stochastic differential equations. Indiana Math. J. 24, 613-625 (1975). | MR 368143 | Zbl 0278.60041

[10] J.B. Walsh : A diffusion with discontinuous local time. Astérisque 52-53, 37-45 (1978).

[11a] P. Lévy : Sur un problème de M. Marcinkiewicz. C.R.A.S. 208 (1939), p. 318-321. Errata p. 776. | JFM 65.0565.01 | Zbl 0020.24202

[11b] P. Lévy : Sur certains processus stochastiques homogènes. Compositio Math., t. 7, 1939, p. 283-339. | JFM 65.1346.02 | Numdam | MR 919 | Zbl 0022.05903

[12] D. Williams : Markov properties of Brownian local time. Bull. Amer. Math. Soc. 75, 1035-1036 (1969). | MR 245095 | Zbl 0266.60060

[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. | MR 45333 | Zbl 0045.07002

[14] M.T. Barlow, J.W. Pitman, M. Yor : On Walsh's Brownian Motions. Dans ce volume. | Numdam | Zbl 0747.60072

[15] M.T. Barlow, J.W. Pitman, M. Yor : Some extensions of the arc sine law. Technical Report n° 189. Department of Statistics, U.C. Berkeley (1989).

[16] J. Kent : Some probabilistic properties of Bessel functions. Ann. Prob. 6, 760-770 (1978). | MR 501378 | Zbl 0402.60080

[17] S.A. Molchanov, E. Ostrovski : Symmetric stable processes as traces of degenerate diffusion processes. Theory of Proba. and its App., vol. XIV, n° 1, 128-131 (1969). | Zbl 0281.60091

[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). | MR 116376 | Zbl 0112.10105