Regularity of irregularities on a brownian path

Samuel James Taylor

Annales de l'institut Fourier (1974)

  • Volume: 24, Issue: 2, page 195-203
  • ISSN: 0373-0956

Abstract

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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.

How to cite

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Taylor, Samuel James. "Regularity of irregularities on a brownian path." Annales de l'institut Fourier 24.2 (1974): 195-203. <http://eudml.org/doc/74172>.

@article{Taylor1974,
abstract = {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.},
author = {Taylor, Samuel James},
journal = {Annales de l'institut Fourier},
language = {eng},
number = {2},
pages = {195-203},
publisher = {Association des Annales de l'Institut Fourier},
title = {Regularity of irregularities on a brownian path},
url = {http://eudml.org/doc/74172},
volume = {24},
year = {1974},
}

TY - JOUR
AU - Taylor, Samuel James
TI - Regularity of irregularities on a brownian path
JO - Annales de l'institut Fourier
PY - 1974
PB - Association des Annales de l'Institut Fourier
VL - 24
IS - 2
SP - 195
EP - 203
AB - 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.
LA - eng
UR - http://eudml.org/doc/74172
ER -

References

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  8. [8] F. B. KNIGHT, Existence of small oscillations at zeros of Brownian motion. Zbl0305.60035
  9. [9] P. LÉVY, Théorie de l'addition des variables aléatoires. Paris, 1937. Zbl0016.17003JFM63.0490.04
  10. [10] P. LÉVY, Le mouvement brownien plan, Amer. J. Math., 62 (1940), 487-550. Zbl0024.13906MR2,107gJFM66.0619.02
  11. [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). Zbl0292.60128MR50 #11486
  12. [12] F. SPITZER, Some theorems concerning two-dimensional Brownian motion, Trans. Amer. Math. Soc., 87 (1958), 187-197. Zbl0089.13601MR21 #3051
  13. [13] S. J. TAYLOR, Exact asymptotic estimates of Brownian path variation, Duke Jour., 39 (1972), 219-241. Zbl0241.60069MR45 #4500

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