@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}, pages = {122--137}, publisher = {Springer - Lecture Notes in Mathematics}, volume = {28}, year = {1994}, mrnumber = {1329108}, zbl = {0810.60076}, language = {en}, url = {http://archive.numdam.org/item/SPS_1994__28__122_0/} }
TY - JOUR AU - Shi, Zhan TI - Liminf behaviours of the windings and Lévy's stochastic areas of planar brownian motion JO - Séminaire de probabilités de Strasbourg PY - 1994 SP - 122 EP - 137 VL - 28 PB - Springer - Lecture Notes in Mathematics UR - http://archive.numdam.org/item/SPS_1994__28__122_0/ LA - en ID - SPS_1994__28__122_0 ER -
%0 Journal Article %A Shi, Zhan %T Liminf behaviours of the windings and Lévy's stochastic areas of planar brownian motion %J Séminaire de probabilités de Strasbourg %D 1994 %P 122-137 %V 28 %I Springer - Lecture Notes in Mathematics %U http://archive.numdam.org/item/SPS_1994__28__122_0/ %G en %F 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://archive.numdam.org/item/SPS_1994__28__122_0/
Handbook of Mathematical Functions. Dover, New York.
& (1965).Large deviations and functional iterated law for diffusion processes. Probab. Th. Rel. Fields 71 435-453. | MR | Zbl
(1986).Windings of spherically symmetric random walks via Brownian embedding. Statist. Probab. Letters 12 345-349. | MR | Zbl
(1991).Loi du logarithme itéré pour certaines intégrales stochastiques. Ann. Sci. Univ. Clermont-Ferrand II Math. 19 9-18. | Numdam | MR | Zbl
(1981).Etude de processus généralisant l'Aire de Lévy. Probab. Th. Rel. Fields 73 463-480. | MR | Zbl
(1986).Comportement asymptotique du nombre de tours effectués par la trajectoire brownienne plane. This volume. | Numdam | Zbl
& (1994a).Asymptotic windings of planar Brownian motion revisited via the Ornstein-Uhlenbeck process. This volume. | Numdam | Zbl
& (1994b).On the maximum partial sums of sequences of independent random variables. Trans. Amer. Math. Soc.64 205-233. | MR | Zbl
(1948).On the lower limits of maxima and minima of Wiener process and partial sums. Z. Wahrscheinlichkeitstheorie verw. Gebiete 43 205-221. | MR | Zbl
(1978).The central limit theorem for windings of Brownian motion and that of plane random walk. Preprint. | MR
(1994).A new proof of Spitzer's result on the winding of two-dimensional Brownian motion. Ann. Probab.10 244-246. | MR | Zbl
(1982).The asymptotic distribution of the range of sums of independent random variables. Ann. Math. Statist.22 427-432. | MR | Zbl
(1951).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.
(1993).The rate of escape for pairs of windings on the Riemann sphere. Proc. London Math. Soc.48 552-564. | Zbl
& . (1993).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
(1985).The "local" law of the iterated logarithm for processes related to Lévy's stochastic area process. Stud. Math.83 229-237. | MR | Zbl
(1986).Diffusion Processes and their Sample paths. 2nd Printing. Springer, Berlin. | Zbl
& . (1974).A note on the Borel-Cantelli lemma. Illinois J. Math.8 248-251. | Zbl
& (1964).Probability in Banach Spaces: Isoperimetry and Processes. Springer, Berlin. | Zbl
& (1991).Wiener's random function, and other Laplacian random functions. Proc. Second Berkeley Symp. Math. Statist. Probab.171-181. | MR | Zbl
(1951).On strong bounds for sums of independent random variables which tend to a stable distribution. Trans. Amer. Math. Soc.81 135-154. | MR | Zbl
(1956).Windings of the plane Brownian motion. Adv. Math.51 212-225. | Zbl
& (1984).On D. Williams' pinching method and some applications. J. London Math. Soc. 26 348-364. | Zbl
& . (1982).A decomposition of Bessel bridges. Z. Wahrscheinlichkeitstheorie verw. Gebiete 59 425-457. | Zbl
& (1982).Asymptotic laws of planar Brownian motion. Ann. Probab.(Special Invited Paper) 14 733-779. | Zbl
& (1986).Further asymptotic laws of planar Brownian motion. Ann. Probab.17 965-1011. | Zbl
& (1989).Diffusions, Markov Processes and Martingales, vol. II: Itô Calculus. Wiley, Chichester. | Zbl
& (1987).Windings of Brownian motion and random walk in R2. Preprint. | MR
(1994).Some theorems concerning 2-dimensional Brownian motion. Trans. Amer. Math. Soc.87 187-197. | MR | Zbl
(1958).A simple geometric proof of Spitzer's winding number formula for 2-dimensional Brownian motion. Univ. College, Swansea. Unpublished.
(1974).Some Aspects of Brownian Motion. Part I: Some Special Functionals. Birkhäuser, Basel. | Zbl
(1992).