Summary
For a strictly stationary random sequence (X i) i≧0 we find sufficient conditions such that the distribution of the last exit time t β = max{i∶ X i>βi} (β>0) tends weakly to a nondegenerate limit distribution as β↓0.
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Hüsler, J. Limit distribution of the last exit time for stationary random sequences. Z. Wahrscheinlichkeitstheorie verw Gebiete 52, 301–308 (1980). https://doi.org/10.1007/BF00538894
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DOI: https://doi.org/10.1007/BF00538894