A universal form of the Chung-type law of the iterated logarithm
Consider an i.i.d. sequence \(X_1,X_2,\dots\) of real-valued random variables, and let \(S_n= X_1+\cdots+ X_n\) \((n= 1,2,\dots)\). A universal Chung-type law of the iterated logarithm is proved, that is, necessary and sufficient conditions for the existence of sequences \((a_n)\) and \((b_n)\) are found (under some side conditions) such that \(0<\liminf_{n\to\infty} b^{-1}_n \max_{j= 1,\dots,n} | S_j- a_j|< \infty\) w.p. 1.
scientific article; zbMATH DE number 1130479