Asymptotic windings of planar brownian motion revisited via the Ornstein-Uhlenbeck process
Séminaire de probabilités de Strasbourg (1994)
- Volume: 28, page 138-152
Access Full Article
topHow to cite
topBertoin, Jean, and Werner, Wendelin. "Asymptotic windings of planar brownian motion revisited via the Ornstein-Uhlenbeck process." Séminaire de probabilités de Strasbourg 28 (1994): 138-152. <http://eudml.org/doc/113869>.
@article{Bertoin1994,
author = {Bertoin, Jean, Werner, Wendelin},
journal = {Séminaire de probabilités de Strasbourg},
keywords = {subordinator; Ornstein-Uhlenbeck process; winding number of the planar Brownian motion},
language = {eng},
pages = {138-152},
publisher = {Springer - Lecture Notes in Mathematics},
title = {Asymptotic windings of planar brownian motion revisited via the Ornstein-Uhlenbeck process},
url = {http://eudml.org/doc/113869},
volume = {28},
year = {1994},
}
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
PB - Springer - Lecture Notes in Mathematics
VL - 28
SP - 138
EP - 152
LA - eng
KW - subordinator; Ornstein-Uhlenbeck process; winding number of the planar Brownian motion
UR - http://eudml.org/doc/113869
ER -
References
top- 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). Zbl0810.60077
- 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]. Zbl0192.55401
- 3. K.L. Chung, 'On the maximum partial sums of sequences of independent random variables', Trans. Amer. Math. Soc.64 (1948) 205-233. Zbl0032.17102
- 4. R. Durrett, 'A new proof of Spitzer's result on the winding of two-dimensional Brownian motion', Ann. Probab.10 (1982) 244-246. Zbl0479.60081
- 5. R. Durrett, 'Brownian motion and martingales in analysis', Wadsworth (1984). Zbl0554.60075
- 6. W.E. Feller, 'A limit theorem for random variables with infinite moments', Amer. J. Math.68 (1946) 257-262. Zbl0060.28704MR16569
- 7. J. Franchi, 'Théorème des résidus stochastique et asymptotique pour 1-formes sur S2', Prépublication du Laboratoire de Probabilités16, 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). Zbl0309.60047MR400406
- 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. Zbl0803.60040MR1241788
- 11. W.M. Hirsch, 'A strong law for the maximum cumulative sum of independent random variables', Comm. Pure Appl. Math.18 (1965) 109-127. Zbl0135.19205MR179828
- 12. J.F. Le Gall and M. Yor, 'Etude asymptotique des enlacements du mouvement brownien autour des droites de l'espace', Probab. Th. Rel. Fields74 (1987) 617-635. Zbl0594.60083MR876259
- 13. J.F. Le Galland M. Yor, 'Enlacements du mouvement brownien autour des courbes de l'espace', Trans. Amer. Math. Soc.317 (1990) 687-722. Zbl0696.60072MR946219
- 14. T.J. Lyons and H.P. McKean, 'Winding of the plane Brownian motion', Adv. Math.51 (1984) 212-225. Zbl0541.60075MR740582
- 15. P. Messulam and M. Yor, 'On D. Williams' pinching method and some applications', J. London Math. Soc.26 (1982) 348-364. Zbl0518.60088MR675178
- 16. J.W. Pitman and M. Yor, 'Asymptotic laws of planar Brownian motion', Ann. Probab.14 (1986) 733-779. Zbl0607.60070MR841582
- 17. W.E. Pruitt and S.J. Taylor, 'Sample path properties of processes with stable component', Z. Wahrscheinlichkeitstheorie verw. Geb.12 (1969) 267-289. Zbl0181.21103MR258126
- 18. D. Revuz and M. Yor, 'Continuous martingales and Brownian motion', Springer (1991). Zbl0731.60002MR1083357
- 19. L.C.G. Rogers and D. Williams, 'Diffusions, Markov processes and Martingales', vol 2: Itô Calculus,Wiley (1987). Zbl0627.60001MR921238
- 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). Zbl0810.60076MR1329108
- 21. F. Spitzer, 'Some theorems concerning 2-dimensional Brownian motion', Trans. Amer. Math. Soc.87 (1958) 187-197. Zbl0089.13601MR104296
- 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. Zbl0747.60076MR1146463
Citations in EuDML Documents
topNotesEmbed ?
topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.