Hostname: page-component-586b7cd67f-2plfb Total loading time: 0 Render date: 2024-11-22T11:53:21.415Z Has data issue: false hasContentIssue false
  • English
  • Français

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.
Get access Rights & Permissions [Opens in a new window]

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 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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