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The exact Hausdorff measure of the level sets of Brownian motion. (English) Zbl 0458.60076


MSC:

60J65 Brownian motion
60J55 Local time and additive functionals
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[1] Burkholder, D. L., Distribution function inequalities for martingales, Ann. Probability, 1, 19-42 (1973) · Zbl 0301.60035
[2] Ito, K.; McKean, H. P., Diffusion Processes and their Sample Paths (1965), Berlin-Heidelberg-New York: Springer, Berlin-Heidelberg-New York · Zbl 0127.09503
[3] Kingman, J. F.C., An intrinsic description of local time, J. London Math. Soc. 6 Ser., 2, 725-731 (1973) · Zbl 0283.60080
[4] Knight, F. B., Random walks and a sojourn density process of Brownian motion, Trans. Amer. Math. Soc., 109, 56-86 (1963) · Zbl 0119.14604
[5] Orey, S.; Taylor, S. J., How often on a Brownian path does the law of the iterated logarithm fail, Proc. London Math. Soc. 28 Ser., 3, 174-192 (1974) · Zbl 0292.60128
[6] Perkins, E.A.: A global intrinsic characterization of local time. [To appear in Ann. Probability] · Zbl 0469.60081
[7] Taylor, S. J., Sample Path Properties of Processes with Stationary Independent Increments, Stochastic Analysis, 387-414 (1973), New York: Wiley, New York
[8] Taylor, S. J.; Wendel, J. G., The exact Hausdorff measure of the zero set of a stable process, Z. Wahrscheinlichkeitstheorie verw. Gebiete, 6, 170-180 (1966) · Zbl 0178.52702
[9] Walsh, J. B., Downcrossings and the Markov property of local time, Temps Locaux, Astérisque 52-53, 89-115 (1978), Paris: Société Mathématique de France, Paris
[10] Williams, D., Lévy’s downcrossing theorem, Z. Wahrscheinlichkeitstheorie verw. Gebiete, 40, 157-158 (1977) · Zbl 0372.60115
[11] Kesten, H., An iterated logarithm law for local time, Duke Math. J., 32, 447-456 (1965) · Zbl 0132.12701
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