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How small are the increments of a Wiener process? (English) Zbl 0387.60032


MSC:

60F15 Strong limit theorems
60G15 Gaussian processes
60G17 Sample path properties
60G50 Sums of independent random variables; random walks
60J65 Brownian motion
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[1] Chung, K. L., On the maximum partial sums of sequences of independent random variables, Trans. Amer. Math. Soc., 64, 205-233 (1948) · Zbl 0032.17102
[2] Csörgő, M.; Révész, P., How big are the increments of a multi-parameter Wiener Process?, Z. Wahrscheinlichkeitstheorie verw. Gebiete, 42, 1-12 (1978) · Zbl 0356.60031
[3] Deo, C. M., Technical Report (1977), University of Ottawa
[4] Dvoretzky, A., On the oscillation of the Brownian motion process, Israel J. Math., 1, 212-214 (1963) · Zbl 0211.48303
[5] Erdös, P.; Rényi, A., On a new law of large numbers, J. Analyse Math., 13, 103-111 (1970) · Zbl 0225.60015
[6] Hirsch, W. M., A strong law for the maximum cumulative sum of independent random variables, Comm. Pure Appl. Math., 18, 109-127 (1965) · Zbl 0135.19205
[7] Jain, N. C.; Pruitt, W. E., The other law of the iterated logarithm, Ann. Probability, 3, 1046-1049 (1975) · Zbl 0319.60031
[8] Lévy, P., Théorie de l’addition des variables aléatories indépendentes (1937), Gauthier-Villars: Gauthier-Villars Paris
[9] Mogul’skiǐ, A. A., Small deviations in a space of trajectories, Theor. Probability Appl., 19, 726-736 (1974) · Zbl 0326.60061
[10] Taylor, S. J., Regularity of irregularities on a Brownian path, Ann. Inst. Fourier, 24, 195-203 (1974), Grenoble · Zbl 0262.60059
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