Summary
If n is large, a plot of log n independent Brownian paths over [0, n] is nearly certain to give the appearance of a shaded region having square root boundaries.
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deAcosta, A.: A new proof of the Hartman-Winter law of the iterated logarithm. Ann. Probab. 11, 270–276 (1983)
LePage, R.: Log log law for Gaussian processes. Z. Wahrscheinlichkeitstheor. Verw. Geb. 25, 103–108 (1973)
McKean, H.P.: Stochastic integrals. New York-London: Academic Press 1969
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Research of this author was partially supported by the National Science Foundation under grant MCS 82-00786
This work was undertaken while B. Schreiber, of Wayne State University, was a Visiting Professor of Mathematics at Michigan State University, whose hospitality he wishes to acknowledge with gratitude.
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LePage, R., Schreiber, B.M. An iterated logarithm law for families of Brownian paths. Z. Wahrscheinlichkeitstheorie verw Gebiete 70, 341–344 (1985). https://doi.org/10.1007/BF00534866
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DOI: https://doi.org/10.1007/BF00534866