Loi de l’indice du lacet Brownien, et distribution de Hartman-Watson. (French) Zbl 0436.60057


60J65 Brownian motion
60H05 Stochastic integrals
33C10 Bessel and Airy functions, cylinder functions, \({}_0F_1\)
60G44 Martingales with continuous parameter
Full Text: DOI


[1] Getoor, R. K.; Sharpe, M. J., Conformal martingales, Invent. Math., 16, 271-308 (1972) · Zbl 0268.60048
[2] Getoor, R. K.; Sharpe, M. J., Excursions of Brownian motion and Bessel processes, Z. Wahrscheinlichkeitstheorie verw. Gebiete, 47, 83-106 (1979) · Zbl 0399.60074
[3] Hartman, P., Completely monotone families of solutions of n th order linear differential equations and infinitely divisible distributions, Ann. S. Norm. Sup. Pisa. IV, III, 267-287 (1976) · Zbl 0386.34016
[4] Hartman, P.; Watson, G. S., “Normal” distribution functions on spheres and the modified Bessel functions, Ann. Probab., 2, 593-607 (1974) · Zbl 0305.60033
[5] Ito, K., Extension of Stochastic integrals, Proc. of Intern. Sympos., 95-109 (1976), Kyoto: SDE, Kyoto
[6] Ito, K.; McKean, H. P., Diffusion processes and their sample paths (1965), Berlin-Heidelberg-New York: Springer, Berlin-Heidelberg-New York · Zbl 0127.09503
[7] Jeulin, T.; Yor, M., Inégalité de Hardy, semi-martingales, et faux-amis. Sém. Probabilités XIII, Lect. Notes in Maths 721 (1979), Berlin-Heidelberg-New York: Springer, Berlin-Heidelberg-New York · Zbl 0419.60049
[8] Kazamaki, N., On a problem of Girsanov, Tohoku Math. J., 29, 597-600 (1977) · Zbl 0381.60040
[9] Kazamaki, N.; Sekiguchi, T., On the transformation of some classes of martingales by a change of law, Tohoku Math. J., 31, 261-279 (1979) · Zbl 0438.60040
[10] Kent, J., Some probabilistic properties of Bessel functions, Ann. Probab., 6, 760-770 (1978) · Zbl 0402.60080
[11] Kent, J., The infinite divisibility of the von Mises-Fisher distribution for all values of the parameter in all dimensions, Proc. London Math. Soc. 3, 35, 359-384 (1977) · Zbl 0355.60015
[12] Mackevicius, V.: Formula for conditional Wiener integrals. Int. Symposium on Stoch. Diff Equations. August 28-Sept. 2, 1978. Vilnius. Abstracts of Communications.
[13] Novikov, A. A., On an identity for stochastic integrals, Theory. Probab. Appl., 17, 717-720 (1972) · Zbl 0284.60054
[14] Petiau, G., La théorie des fonctions de Bessel (1955), Paris: Centre National de la Recherche Scientifique, Paris · Zbl 0067.04704
[15] Pitman, J.W.: The radial and angular parts of Drifting Brownian motion. A paraître.
[16] Yor, M., Formule de Cauchy relative à certains lacets Browniens, Bulletin Soc. Math. France, 105, 3-31 (1977) · Zbl 0375.60068
[17] Spitzer, F., Some theorems concerning 2-dimensional Brownian motion, Trans. Amer. Math. Soc, 87, 187-197 (1958) · Zbl 0089.13601
[18] Ellison, W. J.; Mendes-France, M., Les nombres premiers. Activités scientifiques et industrielles (1975), Paris: Hermann, Paris · Zbl 0313.10001
[19] Perrin, F., Etude mathématique du mouvement Brownien de rotation, Ann. Sci. Ecole Norm. Sup., 45, 1-51 (1928) · JFM 54.0993.05
[20] Edwards, S. F., Statistical mechanics with topological constraints: I, Proc. Phys. Soc., 91, 513-519 (1967) · Zbl 0181.57001
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.