Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
9662428 | Computers & Mathematics with Applications | 2005 | 14 Pages |
Abstract
Let {X, Xn; n ⥠1} be a sequence of i.i.d. random variables. Set Sn = X1 + X2 + ⦠+ Xn and Mn = maxkâ¤n |Sk|, n ⥠1. By using the strong approximation method, we obtain that for any â1 < b ⤠1, limâ¡Îµâ0ε2b+2ân=1â(logâ¡n)bnP(Mnâ¥ÎµÏnlogâ¡n)=2E|N|(2b+2)b+1âk=0â(â1)k(2k+1)2b+2 if and only if Ex = 0 and Ex2 < â, which strengthen and extend the result of Gut and SpÇtaru [1], where N is the standard normal random variable. Furthermore, L2 convergence and a.s. convergence are also discussed.
Related Topics
Physical Sciences and Engineering
Computer Science
Computer Science (General)
Authors
Tian-Xiao Pang, Zheng-Yan Lin,