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Produits semi-directs de diffusions reelles et lois asymptotiques

Published online by Cambridge University Press:  01 July 2016

J. Franchi
J. Franchi*
Affiliation:
Université Paris VI
*
∗Postal address: Laboratoire de Probabilités, Université Paris VI, 4, place Jussieu, Tour 56 3ème Etage, 75252 Paris Cedex 05, France.
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Abstract

A general study of the asymptotic law of a skew-product of two real diffusions is proposed; a complete and elementary form of the Rosenkrantz theorem is given; the results are applied to three examples: the Brownian motions on SO3, on S3, and on SH3.

Keywords

SKEW PRODUCTSREAL DIFFUSIONSASYMPTOTIC LAWS
Type
Research Article
Information
Advances in Applied Probability , Volume 21 , Issue 4 , December 1989 , pp. 756 - 769
Copyright
Copyright © Applied Probability Trust 1989 

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References

Bibliographie

[1] Albeverio, S., Kusuoka, S. Et Streit, L. (1984) Convergence of Dirichlet forms and associated Schrödinger operators. Bielefeld–Bochum–Stochastik no 4.Google Scholar
[2] Brooks, J. K. Et Chacon, R. V. (1983) Diffusions as a limit of stretched Brownian motions. Adv. Math. 49, 109–122.CrossRefGoogle Scholar
[3] Durrett, R. (1982) A new proof of Spitzer's result. Ann. Prob. 10, 244–246.CrossRefGoogle Scholar
[4] Harrison, J. M. Et Shepp, L. A. (1981) On skew Brownian motion. Ann. Prob. 9, 309–313.Google Scholar
[5] Ito, K. Et Mackean, H. P. (1965) Diffusion Processes and their Sample Paths. Springer-Verlag, Berlin.Google Scholar
[6] Kasahara, Y. Et Kotani, S. (1979) Limit processes for a class of additive functionals of recurrent diffusions. Z. Wahrscheinlichkeitsth. 49, 133–153.Google Scholar
[7] Le Gall, J. F. (1984) One dimensional stochastic differential equations involving the local time. Lecture Notes in Mathematics 1095, Springer-Verlag, Berlin, 51–82.Google Scholar
[8] Le Gall, J. F. Et Yor, M. (1986) Etude asymptotique de certains mouvements brownians complexes avec drift. Prob. Theory Rel. Fields 71, 183–229.Google Scholar
[9] Lyons, T. Et Mackean, H. P. (1984) Windings of the plane Brownian motion. Adv. Math. 51, 212–225.CrossRefGoogle Scholar
[10] Messulam, P. Et Yor, M. (1982) On D. Williams' ‘pinching method’ and some applications. J. London Math. Soc. 26, 348–364.CrossRefGoogle Scholar
[11] Pitman, J. W. Et Yor, M. (1984) The asymptotic joint distribution of windings of planar Brownian motion. Bull. Amer. Math. Soc. 10, 109–111.Google Scholar
[12] Pitman, J. W. Et Yor, M. (1986) Asymptotic laws of planar Brownian motion. Ann. Prob. 14, 733–779.Google Scholar
[13] Rosenkrantz, W. (1975) Limit theorems for solutions to a class of stochastic differential equations. Indiana Univ. Math. J. 24, 613–625.Google Scholar
[14] Spitzer, F. (1958) Some theorems concerning two-dimensional Brownian motion. Trans. Amer. Math. Soc. 87, 187–197.Google Scholar
[15] Walsh, J. B. (1978) A diffusion with discontinuous local time. Astérisque 52–53, 37–45.Google Scholar