Asymptotic windings of planar brownian motion revisited via the Ornstein-Uhlenbeck process
Bertoin, Jean ; Werner, Wendelin
Séminaire de probabilités de Strasbourg, Tome 28 (1994), p. 138-152 / Harvested from Numdam
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@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},
     volume = {28},
     year = {1994},
     pages = {138-152},
     mrnumber = {1329109},
     zbl = {0814.60080},
     language = {en},
     url = {http://dml.mathdoc.fr/item/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://gdmltest.u-ga.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). | Numdam | Zbl 0810.60077

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 233420 | Zbl 0192.55401

3. K.L. Chung, 'On the maximum partial sums of sequences of independent random variables', Trans. Amer. Math. Soc.64 (1948) 205-233. | MR 26274 | Zbl 0032.17102

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 637391 | Zbl 0479.60081

5. R. Durrett, 'Brownian motion and martingales in analysis', Wadsworth (1984). | MR 750829 | Zbl 0554.60075

6. W.E. Feller, 'A limit theorem for random variables with infinite moments', Amer. J. Math. 68 (1946) 257-262. | MR 16569 | Zbl 0060.28704

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 400406 | Zbl 0309.60047

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 1241788 | Zbl 0803.60040

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 179828 | Zbl 0135.19205

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 876259 | Zbl 0594.60083

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 946219 | Zbl 0696.60072

14. T.J. Lyons and H.P. Mckean, 'Winding of the plane Brownian motion', Adv. Math.51 (1984) 212-225. | MR 740582 | Zbl 0541.60075

15. P. Messulam and M. Yor, 'On D. Williams' pinching method and some applications', J. London Math. Soc.26 (1982) 348-364. | MR 675178 | Zbl 0518.60088

16. J.W. Pitman and M. Yor, 'Asymptotic laws of planar Brownian motion', Ann. Probab.14 (1986) 733-779. | MR 841582 | Zbl 0607.60070

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 258126 | Zbl 0181.21103

18. D. Revuz and M. Yor, 'Continuous martingales and Brownian motion', Springer (1991). | MR 1083357 | Zbl 0731.60002

19. L.C.G. Rogers and D. Williams, 'Diffusions, Markov processes and Martingales', vol 2: Itô Calculus,Wiley (1987). | MR 921238 | Zbl 0627.60001

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). | Numdam | MR 1329108 | Zbl 0810.60076

21. F. Spitzer, 'Some theorems concerning 2-dimensional Brownian motion', Trans. Amer. Math. Soc.87 (1958) 187-197. | MR 104296 | Zbl 0089.13601

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 1146463 | Zbl 0747.60076