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Abstract
We establish some large increment results for partial sum processes of a dependent stationary Gaussian sequence via estimating upper bounds of large deviation probabilities on suprema of the Gaussian sequence.
Abstract
We establish strong limsup theorems related to the law of the iterated logarithm (LIL) for finite dimensional Gaussian random fields by using the second Borel-Cantelli lemma.
Summary An integral analogue of the general almost sure limit theorem is presented. In the theorem, instead of a sequence of random elements, a continuous time random process is involved, moreover, instead of the logarithmical average, the integral of delta-measures is considered. Then the general theorem is applied to obtain almost sure versions of limit theorems for semistable and max-semistable processes, moreover for processes being in the domain of attraction of a stable law or being in the domain of geometric partial attraction of a semistable or a max-semistable law.
SENETA, E., Regularly varying functions , Lecture Notes in Mathematics, Vol. 508, Springer-Verlag, Berlin-New York, 1976. MR 56 # 12189. Russian edition: Pravil'no menyayushchiesya funktsii , Nauka, Moskva, 1985. MR 86m :26001
