STRONG LAWS OF LARGE NUMBERS FOR THE SEQUENCE OF THE
MAXIMUM OF PARTIAL SUMS OF I.I.D. RANDOM VARIABLES
Abstract: Let , let be a sequence of independent copies of a
real-valued random variable , and set , . Motivated by a
theorem of Mikosch (1984), this note is devoted to establishing a strong law of large numbers
for the sequence . More specifically, necessary and sufficient
conditions are given for
where , .
2000 AMS Mathematics Subject Classification: Primary: 60F15; Secondary: 60G50,
Keywords and phrases: Theorem of Mikosch, i.i.d. real-valued random variables,
maximum of partial sums, strong law of large numbers.