Almost sure limiting behaviour of first crossing points of Gaussian sequences |
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| Authors: | Jürg Hüsler |
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| Institution: | Department of Mathematics and Statistics, University of Pittsburgh, Pittsburgh, PA 15260 U.S.A. |
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| Abstract: | Let {Kk,k∈Z} be a stationary, normalized Gaussian sequence and define τβ=min(k:Xk>?βk} the first crossing point of the Gaussian sequence with the moving boundary ?βt. For β→0 we discuss in this paper the a.s. stability, the a.s. relative ability of τβ and an iterated logarithm law for τβ, depending on the correlation function. |
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| Keywords: | stationary Gaussian sequences a s relative stability a s stability law of iterated logarithm |
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