Asymptotic windings of planar brownian motion revisited via the Ornstein-Uhlenbeck process
Séminaire de probabilités de Strasbourg, Tome 28 (1994), pp. 138-152.
@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://archive.numdam.org/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://archive.numdam.org/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://archive.numdam.org/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://archive.numdam.org/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). | EuDML | Numdam | Zbl

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]. | MR | Zbl

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

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

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

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

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). | MR | Zbl

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. | MR | Zbl

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

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. | MR | Zbl

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. | MR | Zbl

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

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

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

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

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

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

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). | EuDML | Numdam | MR | Zbl

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

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. | MR | Zbl