A supplement to the Davis–Gut law |
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| Authors: | Deli Li Andrew Rosalsky |
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| Affiliation: | aDepartment of Mathematical Sciences, Lakehead University, Thunder Bay, Ontario, Canada P7B 5E1;bDepartment of Statistics, University of Florida, Gainesville, FL 32611, USA |
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| Abstract: | Let {X,Xn;n 1} be a sequence of i.i.d. real-valued random variables and set  , n1. Let h( ) be a positive nondecreasing function such that  . Define Lt=logemax{e,t} for t0. In this note we prove that if and only if E(X)=0 and E(X2)=1, where  , t1. When h(t)≡1, this result yields what is called the Davis–Gut law. Specializing our result to h(t)=(Lt)r, 0<r 1, we obtain an analog of the Davis–Gut law. |
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| Keywords: | Davis– Gut law Law of the iterated logarithm Partial sums of i.i.d. random variables |
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