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

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.

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.

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     title = {Regularity of irregularities on a brownian path},
     journal = {Annales de l'Institut Fourier},
     pages = {195--203},
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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] 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

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