On a standard Brownian motion path there are points where the local behaviour is different from the pattern which occurs at a fixed with probability 1. This paper is a survey of recent results which quantity the extent of the irregularities and show that the exceptional points themselves occur in an extremely regular manner.
Sur la trajectoire d’un mouvement brownien, il y a des points où la conduite locale diffère du modèle qui arrive à un point fixé avec probabilité 1. Cette conférence est une revue des résultats récents qui mesurent l’étendue des irrégularités et montrent que les points exceptionnels arrivent dans une manière très régulière.
@article{AIF_1974__24_2_195_0, author = {Taylor, Samuel James}, title = {Regularity of irregularities on a brownian path}, journal = {Annales de l'Institut Fourier}, pages = {195--203}, publisher = {Institut Fourier}, address = {Grenoble}, volume = {24}, number = {2}, year = {1974}, doi = {10.5802/aif.513}, mrnumber = {53 #14699}, zbl = {0262.60059}, language = {en}, url = {http://archive.numdam.org/articles/10.5802/aif.513/} }
TY - JOUR AU - Taylor, Samuel James TI - Regularity of irregularities on a brownian path JO - Annales de l'Institut Fourier PY - 1974 SP - 195 EP - 203 VL - 24 IS - 2 PB - Institut Fourier PP - Grenoble UR - http://archive.numdam.org/articles/10.5802/aif.513/ DO - 10.5802/aif.513 LA - en ID - AIF_1974__24_2_195_0 ER -
Taylor, Samuel James. Regularity of irregularities on a brownian path. Annales de l'Institut Fourier, Volume 24 (1974) no. 2, pp. 195-203. doi : 10.5802/aif.513. http://archive.numdam.org/articles/10.5802/aif.513/
[1] On the Lipchitz's condition for Brownian motion, J. Math. Soc. Japan, 11 (1959), 263-274. | Zbl
, and ,[2] First passage times and sojourn times for Brownian motion in space, Trans. Amer. Math. Soc., 103 (1962), 434-450. | MR | Zbl
and ,[3] On the oscillation of the Brownian motion process, Israel J. Math., 1 (1963), 212-214. | MR | Zbl
,[4] Some problems on random walk in space, Proc. Second Berkeley Symposium (1951), 353-367. | MR | Zbl
and ,[5] Strong and weak Φ-variation, Notices Amer. Math. Soc., 19 (1972), 405. | MR | Zbl
and ,[6] A lower Lipchitz condition for the stable subordinator, Z fur Wahrscheinlichkeitstheorie, 17 (1971), 23-32. | MR | Zbl
,[7] Local asymptotic laws for Brownian motion, Annals of Probability, 1 (1973), 527-549. | MR | Zbl
and ,[8] Existence of small oscillations at zeros of Brownian motion. | Numdam | Zbl
,[9] Théorie de l'addition des variables aléatoires. Paris, 1937. | JFM | Zbl
,[10] Le mouvement brownien plan, Amer. J. Math., 62 (1940), 487-550. | JFM | MR | Zbl
,[11] How often on a Brownian path does the law of iterated logarithm fail ? Proc. Lon. Math. Soc., 28 (3), (1974). | MR | Zbl
and ,[12] Some theorems concerning two-dimensional Brownian motion, Trans. Amer. Math. Soc., 87 (1958), 187-197. | MR | Zbl
,[13] Exact asymptotic estimates of Brownian path variation, Duke Jour., 39 (1972), 219-241. | MR | Zbl
,Cited by Sources: