# SMALL BALL AND LARGE DEVIATION PROBABILITIES ESTIMATES FOR GAUSSIAN PROCESSES WITH STATIONARY INCREMENTS

• Lee, Seaung-Hyune ;
• Choi, Yong-Kab ;
• Oh, Ho-Se
• Published : 1999.03.01
• 24 4

#### Abstract

In this paper we obtain sharp upper and lower bounds of samll ball and large deviation probabilities for the increments of Gaussian processes with stationary increments, whose results are essential to establish Chung type laws of iteratted logarithm.

#### Keywords

small ball probability;large deviation probability;law of iterated logarithm;Gaussian process;stationary increments, Borel-Cantelli lemma

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