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

MSC:
60J65 Brownian motion
60H05 Stochastic integrals
33C10 Bessel and Airy functions, cylinder functions, \({}_0F_1\)
60G44 Martingales with continuous parameter
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[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, Vol 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. SDE. Kyoto, pp. 95-109 (1976)
[6] Ito, K., McKean, H.P.: Diffusion processes and their sample paths. Berlin-Heidelberg-New York: Springer 1965 · Zbl 0127.09503
[7] Jeulin, T., Yor, M.: Inégalité de Hardy, semi-martingales, et faux-amis. Sém. Probabilités XIII. Lect. Notes in Maths 721. Berlin-Heidelberg-New York: Springer 1979 · 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. Centre National de la Recherche Scientifique. Paris (1955). · 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. Paris: Hermann (1975)
[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
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