Let X1, X2,… be independent, but not necessarily identically distributed random variables in the domain of attraction of a stable law with index 0<a<2. This paper uses Mn=max 1?i?n|Xi| to establish a self-normalized law of the iterated logarithm (LIL) for partial sums. Similarly self-normalized increments of partial sums are studied as well. In particular, the results of self-normalized sums of Horváth and Shaounder independent and identically distributed random variables are extended and complemented. As applications, some corresponding results for self-normalized weighted sums of iid random variables are also concluded.
Strassen, V., A converse to the law of the iterated logarithm, Z. Wahrsch. verw. Gebiete, 4 (1966), 265-268. MR 2000d:60046
'A converse to the law of the iterated logarithm' () 4Z. Wahrsch. verw. Gebiete: 265-268.
A converse to the law of the iterated logarithmZ. Wahrsch. verw. Gebiete4265268)| false