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Rates of clustering in Strassen's LIL for Brownian motion (1991)

Goodman, Victor ; Kuelbs, J.

Springer

Journal of theoretical probability 4 (1991), S. 285-309

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ISSN: 1572-9230

Keywords: Brownian motion ; rates of clustering ; Strassen's LIL

Source: Springer Online Journal Archives 1860-2000

Topics: Mathematics

Notes: Abstract If {W(t): 0≦t≦∞} denotes standard Brownian motion and then with probability one the random sequence $$\{ W(n( \cdot ))/(2nL_2 n)^{1/2} :n \geqslant 1\} $$ converges to and clusters throughoutK in the uniform norm. This is Strassen's LIL for Brownian motion, and here we examine the rate at which this convergence and clustering takes place, improving some results of K. Grill.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1007/BF01258738

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