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On the Spitzer and Chung laws of the iterated logarithm for Brownian motion

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References

  • Chung, K.L. (1948): On the maximum partial sums of sequences of independent random variables. Trans. Amer. Math. Soc. 64, 205–233.

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  • Ciesielski, Z. & Taylor, S.J. (1962). First passage times and sojourn times for Brownian motion in space and the exact Hausdorff measure of the sample path. Trans. Amer. Math. Soc. 103 434–450.

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  • Fristedt, B.E. (1974): Sample functions of stochastic processes with stationary independent increments. In: Advances in Probability 3 (Eds.: P. Ney & S. Port) pp. 241–396. Dekker, New York.

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  • Itô, K. & McKean, H.P. (1965): Diffusion Processes and their Sample Paths. Springer, Berlin.

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  • Ledoux, M. & Talagrand, M. (1991): Probability in Banach Spaces: Isoperimetry and Processes. Springer, Berlin.

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  • Lévy, P. (1953): La mesure de Hausdorff de la courbe du mouvement brownien. Giornale dell’Istituto Italiano degli Attuari 16 1–37.

    MathSciNet  MATH  Google Scholar 

  • Révész, P. (1990): Random Walk in Random and Non-Random Environments. World Scientific, Singapore.

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  • Revuz, D. & Yor, M. (1994): Continuous Martingales and Brownian Motion. 2nd Edition. Springer, Berlin.

    MATH  Google Scholar 

  • Spitzer, F. (1958): Some theorems concerning 2-dimensional Brownian motion. Trans. Amer. Math. Soc. 87 187–197.

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Jacques Azéma Michel Emery Paul André Meyer Marc Yor

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© 1995 Springer-Verlag

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Gruet, JC., Shi, Z. (1995). On the Spitzer and Chung laws of the iterated logarithm for Brownian motion. In: Azéma, J., Emery, M., Meyer, P.A., Yor, M. (eds) Séminaire de Probabilités XXIX. Lecture Notes in Mathematics, vol 1613. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0094216

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  • DOI: https://doi.org/10.1007/BFb0094216

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  • Print ISBN: 978-3-540-60219-4

  • Online ISBN: 978-3-540-44744-3

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