Geodesic
Asymptotic windings of planar brownian motion revisited via the Ornstein-Uhlenbeck process
Séminaire de probabilités de Strasbourg, Tome 28 (1994), pp. 138-152.

Voir la notice de l'acte provenant de la source Numdam

@article{SPS_1994__28__138_0,
     author = {Bertoin, Jean and Werner, Wendelin},
     title = {Asymptotic windings of planar brownian motion revisited via the {Ornstein-Uhlenbeck} process},
     journal = {S\'eminaire de probabilit\'es de Strasbourg},
     pages = {138--152},
     publisher = {Springer - Lecture Notes in Mathematics},
     volume = {28},
     year = {1994},
     mrnumber = {1329109},
     zbl = {0814.60080},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SPS_1994__28__138_0/}
}
TY  - JOUR
AU  - Bertoin, Jean
AU  - Werner, Wendelin
TI  - Asymptotic windings of planar brownian motion revisited via the Ornstein-Uhlenbeck process
JO  - Séminaire de probabilités de Strasbourg
PY  - 1994
SP  - 138
EP  - 152
VL  - 28
PB  - Springer - Lecture Notes in Mathematics
UR  - http://geodesic.mathdoc.fr/item/SPS_1994__28__138_0/
LA  - en
ID  - SPS_1994__28__138_0
ER  - 
%0 Journal Article
%A Bertoin, Jean
%A Werner, Wendelin
%T Asymptotic windings of planar brownian motion revisited via the Ornstein-Uhlenbeck process
%J Séminaire de probabilités de Strasbourg
%D 1994
%P 138-152
%V 28
%I Springer - Lecture Notes in Mathematics
%U http://geodesic.mathdoc.fr/item/SPS_1994__28__138_0/
%G en
%F SPS_1994__28__138_0
Bertoin, Jean; Werner, Wendelin. Asymptotic windings of planar brownian motion revisited via the Ornstein-Uhlenbeck process. Séminaire de probabilités de Strasbourg, Tome 28 (1994), pp. 138-152. http://geodesic.mathdoc.fr/item/SPS_1994__28__138_0/

1. J. Bertoin and W. Werner, 'Comportement asymptotique du nombre de tours effectués par la trajectoire brownienne plane', Séminaire de Probabilités XXVIII, Lect. Notes in Math., Springer (1994). | Zbl | mathdoc-id | EuDML

2. L. Breiman, 'A delicate law of the iterated logarithm for non-decreasing stable processes', Ann. Math. Statist. 39 (1968) 1818-1824. [correction id. 41 (1970) 1126-1127]. | Zbl | MR

3. K.L. Chung, 'On the maximum partial sums of sequences of independent random variables', Trans. Amer. Math. Soc.64 (1948) 205-233. | Zbl | MR

4. R. Durrett, 'A new proof of Spitzer's result on the winding of two-dimensional Brownian motion', Ann. Probab. 10 (1982) 244-246. | Zbl | MR

5. R. Durrett, 'Brownian motion and martingales in analysis', Wadsworth (1984). | Zbl | MR

6. W.E. Feller, 'A limit theorem for random variables with infinite moments', Amer. J. Math. 68 (1946) 257-262. | Zbl | MR

7. J. Franchi, 'Théorème des résidus stochastique et asymptotique pour 1-formes sur S2', Prépublication du Laboratoire de Probabilités 16, Université de Paris VI (1989).

8. B.E. Fristedt, 'Sample functions of stochastic processes with stationary independent increments', Advances in ProbabilityIII, P. Ney, S. Port (eds)241-396, Dekker (1974). | Zbl | MR

9. J.C. Gruet, 'Enroulement du mouvement brownien plan autour de deux points', Thèse de Doctorat, Université de Paris VI (1990).

10. J.C. Gruet and T.S. Mountford, 'The rate of escape for pairs of windings on the Riemann sphere', J. London Math. Soc. (2) 48 (1993) 552-564. | Zbl | MR

11. W.M. Hirsch, 'A strong law for the maximum cumulative sum of independent random variables', Comm. Pure Appl. Math.18 (1965) 109-127. | Zbl | MR

12. J.F. Le Gall and M. Yor, 'Etude asymptotique des enlacements du mouvement brownien autour des droites de l'espace', Probab. Th. Rel. Fields 74 (1987) 617-635. | Zbl | MR

13. J.F. Le Gall and M. Yor, 'Enlacements du mouvement brownien autour des courbes de l'espace', Trans. Amer. Math. Soc.317 (1990) 687-722. | Zbl | MR

14. T.J. Lyons and H.P. Mckean, 'Winding of the plane Brownian motion', Adv. Math.51 (1984) 212-225. | Zbl | MR

15. P. Messulam and M. Yor, 'On D. Williams' pinching method and some applications', J. London Math. Soc.26 (1982) 348-364. | Zbl | MR

16. J.W. Pitman and M. Yor, 'Asymptotic laws of planar Brownian motion', Ann. Probab.14 (1986) 733-779. | Zbl | MR

17. W.E. Pruitt and S.J. Taylor, 'Sample path properties of processes with stable component', Z. Wahrscheinlichkeitstheorie verw. Geb.12 (1969) 267-289. | Zbl | MR

18. D. Revuz and M. Yor, 'Continuous martingales and Brownian motion', Springer (1991). | Zbl | MR

19. L.C.G. Rogers and D. Williams, 'Diffusions, Markov processes and Martingales', vol 2: Itô Calculus,Wiley (1987). | Zbl | MR

20. Z. Shi, 'Liminf behaviours of the windings and Lévy's stochastic area of planar Brownian motion', Séminaire de Probabilités XXVIII, Lect. Notes in Math., Springer (1994). | mathdoc-id | Zbl | MR | EuDML

21. F. Spitzer, 'Some theorems concerning 2-dimensional Brownian motion', Trans. Amer. Math. Soc.87 (1958) 187-197. | Zbl | MR

22. D. Williams, 'A simple geometric proof of Spitzer's winding number formula for 2-dimensional Brownian motion', unpublished paper, University College of Swansea (1974).

23. M. Yor, 'Etude asymptotique des nombres de tours de plusieurs mouvements complexes corrélés', in Random walks, Brownian motion and interacting particle systems, Prog. Probab. 28, Birkhäuser (1991) 441-455. | Zbl | MR