Liminf behaviours of the windings and Lévy's stochastic areas of planar brownian motion
Shi, Zhan
Séminaire de probabilités de Strasbourg, Tome 28 (1994), p. 122-137 / Harvested from Numdam
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@article{SPS_1994__28__122_0,
     author = {Shi, Zhan},
     title = {Liminf behaviours of the windings and L\'evy's stochastic areas of planar brownian motion},
     journal = {S\'eminaire de probabilit\'es de Strasbourg},
     volume = {28},
     year = {1994},
     pages = {122-137},
     mrnumber = {1329108},
     zbl = {0810.60076},
     language = {en},
     url = {http://dml.mathdoc.fr/item/SPS_1994__28__122_0}
}

Shi, Zhan. Liminf behaviours of the windings and Lévy's stochastic areas of planar brownian motion. Séminaire de probabilités de Strasbourg, Tome 28 (1994) pp. 122-137. http://gdmltest.u-ga.fr/item/SPS_1994__28__122_0/

Abramowitz, M. & Stegun, I.A. (1965). Handbook of Mathematical Functions. Dover, New York.

Baldi, P. (1986). Large deviations and functional iterated law for diffusion processes. Probab. Th. Rel. Fields 71 435-453. | MR 824713 | Zbl 0587.60074

Bélisle, C. (1991). Windings of spherically symmetric random walks via Brownian embedding. Statist. Probab. Letters 12 345-349. | MR 1131063 | Zbl 0803.60062

Berthuet, R. (1981). Loi du logarithme itéré pour certaines intégrales stochastiques. Ann. Sci. Univ. Clermont-Ferrand II Math. 19 9-18. | Numdam | MR 645559 | Zbl 0491.60031

Berthuet, R. (1986). Etude de processus généralisant l'Aire de Lévy. Probab. Th. Rel. Fields 73 463-480. | MR 859843 | Zbl 0597.60071

Bertoin, J. & Werner, W. (1994a). Comportement asymptotique du nombre de tours effectués par la trajectoire brownienne plane. This volume. | Numdam | Zbl 0810.60077

Bertoin, J. & Werner, W. (1994b). Asymptotic windings of planar Brownian motion revisited via the Ornstein-Uhlenbeck process. This volume. | Numdam | Zbl 0814.60080

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

Csáki, E. (1978). On the lower limits of maxima and minima of Wiener process and partial sums. Z. Wahrscheinlichkeitstheorie verw. Gebiete 43 205-221. | MR 494527 | Zbl 0372.60113

Dorofeev, E.A. (1994). The central limit theorem for windings of Brownian motion and that of plane random walk. Preprint. | MR 1267472

Durrett, R. (1982). A new proof of Spitzer's result on the winding of two-dimensional Brownian motion. Ann. Probab.10 244-246. | MR 637391 | Zbl 0479.60081

Feller, W. (1951). The asymptotic distribution of the range of sums of independent random variables. Ann. Math. Statist.22 427-432. | MR 42626 | Zbl 0043.34201

Franchi, J. (1993). Comportement asymptotique presque sûr des nombres de tours effectués par le mouvement brownien d'une variété riemannienne compacte de dimension 2 ou 3. Technical Report No. 189, Laboratoire de Probabilités Université Paris VI. April 1993.

Gruet, J.-C. & Mountford, T.S.. (1993). The rate of escape for pairs of windings on the Riemann sphere. Proc. London Math. Soc.48 552-564. | Zbl 0803.60040

Helmes, K. (1985). On Lévy's area process. In: Stochastic Differential Systems (Eds.: N. Christopeit, K. Helmes & M. Kohlmann. Lect. Notes Control Inform. Sci. 78 187-194. Springer, Berlin. | Zbl 0609.60041

Helmes, K. (1986). The "local" law of the iterated logarithm for processes related to Lévy's stochastic area process. Stud. Math.83 229-237. | MR 850825 | Zbl 0614.60025

Itô, K. & Mckean, H.P.. (1974). Diffusion Processes and their Sample paths. 2nd Printing. Springer, Berlin. | Zbl 0285.60063

Kochen, S. & Stone, C. (1964). A note on the Borel-Cantelli lemma. Illinois J. Math.8 248-251. | Zbl 0139.35401

Ledoux, M. &Talagrand, M. (1991). Probability in Banach Spaces: Isoperimetry and Processes. Springer, Berlin. | Zbl 0748.60004

Lévy, P. (1951). Wiener's random function, and other Laplacian random functions. Proc. Second Berkeley Symp. Math. Statist. Probab.171-181. | MR 44774 | Zbl 0044.13802

Lipschutz, M. (1956). On strong bounds for sums of independent random variables which tend to a stable distribution. Trans. Amer. Math. Soc.81 135-154. | MR 77015 | Zbl 0073.12502

Lyons, T. & Mckean, H.P. (1984). Windings of the plane Brownian motion. Adv. Math.51 212-225. | Zbl 0541.60075

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

Pitman, J.W. & Yor, M.. (1982). A decomposition of Bessel bridges. Z. Wahrscheinlichkeitstheorie verw. Gebiete 59 425-457. | Zbl 0484.60062

Pitman, J.W. & Yor, M. (1986). Asymptotic laws of planar Brownian motion. Ann. Probab.(Special Invited Paper) 14 733-779. | Zbl 0607.60070

Pitman, J.W. & Yor, M. (1989). Further asymptotic laws of planar Brownian motion. Ann. Probab.17 965-1011. | Zbl 0686.60085

Rogers, L.C.G. & Williams, D. (1987). Diffusions, Markov Processes and Martingales, vol. II: Itô Calculus. Wiley, Chichester. | Zbl 0627.60001

Shi, Z. (1994). Windings of Brownian motion and random walk in R2. Preprint. | MR 1617043

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

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

Yor, M. (1992). Some Aspects of Brownian Motion. Part I: Some Special Functionals. Birkhäuser, Basel. | Zbl 0779.60070