A supplement to the Davis–Gut law |
| |
| Authors: | Deli Li Andrew Rosalsky |
| |
| Institution: | aDepartment of Mathematical Sciences, Lakehead University, Thunder Bay, Ontario, Canada P7B 5E1;bDepartment of Statistics, University of Florida, Gainesville, FL 32611, USA |
| |
| 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. |
| |
| Keywords: | Davis– Gut law Law of the iterated logarithm Partial sums of i i d random variables |
| 本文献已被 ScienceDirect 等数据库收录！ |
|
