On limit distributions of first crossing points of Gaussian sequences |
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Authors: | J Hüsler |
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Institution: | Dept. of Math. Statistics, University of Berne, Sidlerstr. 5, CH-3007 Berne, Switzerland |
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Abstract: | Let {Xk, k?Z} be a stationary Gaussian sequence with EX1 – 0, EX2k = 1 and EX0Xk = rk. Define τx = inf{k: Xk >– βk} the first crossing point of the Gaussian sequence with the function – βt (β > 0). We consider limit distributions of τx as β→0, depending on the correlation function rk. We generalize the results for crossing points τx = inf{k: Xk >β?(k)} with ?(– t)?tγL(t) for t→∞, where γ > 0 and L(t) varies slowly. |
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