Regularity of irregularities on a brownian path
Annales de l'Institut Fourier, Tome 24 (1974) no. 2, pp. 195-203.

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 t 0 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.

On a standard Brownian motion path there are points where the local behaviour is different from the pattern which occurs at a fixed t 0 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.

@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},
     zbl = {0262.60059},
     mrnumber = {53 #14699},
     language = {en},
     url = {https://aif.centre-mersenne.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  - https://aif.centre-mersenne.org/articles/10.5802/aif.513/
DO  - 10.5802/aif.513
LA  - en
ID  - AIF_1974__24_2_195_0
ER  - 
%0 Journal Article
%A Taylor, Samuel James
%T Regularity of irregularities on a brownian path
%J Annales de l'Institut Fourier
%D 1974
%P 195-203
%V 24
%N 2
%I Institut Fourier
%C Grenoble
%U https://aif.centre-mersenne.org/articles/10.5802/aif.513/
%R 10.5802/aif.513
%G en
%F AIF_1974__24_2_195_0
Taylor, Samuel James. Regularity of irregularities on a brownian path. Annales de l'Institut Fourier, Tome 24 (1974) no. 2, pp. 195-203. doi : 10.5802/aif.513. https://aif.centre-mersenne.org/articles/10.5802/aif.513/

[1] K. L. Chung, P. Erdös and T. Sirao, On the Lipchitz's condition for Brownian motion, J. Math. Soc. Japan, 11 (1959), 263-274. | Zbl

[2] Z. Ciesielski and S. J. Taylor, First passage times and sojourn times for Brownian motion in space, Trans. Amer. Math. Soc., 103 (1962), 434-450. | MR | Zbl

[3] A. Dvoretzky, On the oscillation of the Brownian motion process, Israel J. Math., 1 (1963), 212-214. | MR | Zbl

[4] A. Dvoretzky and P. Erdös, Some problems on random walk in space, Proc. Second Berkeley Symposium (1951), 353-367. | MR | Zbl

[5] C. Goffman and J. J. Loughlin, Strong and weak Φ-variation, Notices Amer. Math. Soc., 19 (1972), 405. | MR | Zbl

[6] J. Hawkes, A lower Lipchitz condition for the stable subordinator, Z fur Wahrscheinlichkeitstheorie, 17 (1971), 23-32. | MR | Zbl

[7] N. Jain and S. J. Taylor, Local asymptotic laws for Brownian motion, Annals of Probability, 1 (1973), 527-549. | MR | Zbl

[8] F. B. Knight, Existence of small oscillations at zeros of Brownian motion. | Numdam | Zbl

[9] P. Lévy, Théorie de l'addition des variables aléatoires. Paris, 1937. | JFM | Zbl

[10] P. Lévy, Le mouvement brownien plan, Amer. J. Math., 62 (1940), 487-550. | JFM | MR | Zbl

[11] S. Orey and S. J. Taylor, How often on a Brownian path does the law of iterated logarithm fail ? Proc. Lon. Math. Soc., 28 (3), (1974). | MR | Zbl

[12] F. Spitzer, Some theorems concerning two-dimensional Brownian motion, Trans. Amer. Math. Soc., 87 (1958), 187-197. | MR | Zbl

[13] S. J. Taylor, Exact asymptotic estimates of Brownian path variation, Duke Jour., 39 (1972), 219-241. | MR | Zbl

Cité par Sources :