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Almost sure limiting behaviour of first crossing points of Gaussian sequences

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  • Hüsler, Jürg

Abstract

Let {Kk,k[set membership, variant]Z} be a stationary, normalized Gaussian sequence and define [tau][beta]=min(k:Xk>-[beta]k} the first crossing point of the Gaussian sequence with the moving boundary -[beta]t. For [beta]-->0 we discuss in this paper the a.s. stability, the a.s. relative ability of [tau][beta] and an iterated logarithm law for [tau][beta], depending on the correlation function.

Suggested Citation

  • Hüsler, Jürg, 1979. "Almost sure limiting behaviour of first crossing points of Gaussian sequences," Stochastic Processes and their Applications, Elsevier, vol. 8(3), pages 315-321, May.
    • Handle: RePEc:eee:spapps:v:8:y:1979:i:3:p:315-321
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