Chover’s Law of the Iterated Logarithm for Trimmed Sums

Consider a sequence of independent and identically distributed random vari-ables with the underlying distribution in the domain of attraction of a stable distribution with an exponent in (0, 2]. Define the trimmed sums as the par-tial sums excluding r largest observations in magnitude, where r is a fixed integer. This paper proves that Chover’s law of the iterated logarithm holds for the trimmed sums. AMS (2000) subject classification. Primary 60F15