A relation between Chung's and Strassen's laws of the iterated logarithm |
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| Authors: | E Csáki |
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| Institution: | (1) Mathematical Institute of the Hungarian Academy of Sciences, Reáltanoda u. 13–15, H-1053 Budapest, Hungary |
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| Abstract: | Summary Let W(t) be a standard Wiener process and let f(x) be a function from the compact class in Strassen's law of the iterated logarithm. We investigate the lim inf behavior of the variable sup ¦W(xT)(2T loglog T)–1/2–f(x)¦, 0 x1 suitably normalized as T  .This extends Chung's result valid for f(x) 0, stating that lim inf. sup ¦(2T loglogT)–1/2
W(xT)¦(loglog T)–1]= /4 a.s. T 0x1 |
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