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摘要
Let {X-n, n >= 1} be Gaussian random variables with means 0, variances 1, and correlations r(ij) = EXiXj. Suppose there exists a sequence 0 <= rho(n) < 1, n >= 1, such that vertical bar r(ij)vertical bar <= (rho vertical bar j-i vertical bar) for i not equal j, and rho(n) log n(log log n)(1+epsilon) = O(1) as n -> infinity. For a sequence of levels {u(nk), 1 <= k <= n, n >= 1}, let lambda(n) = min(1 <= k <= n) u(nk), and suppose further that n(1 - Phi(lambda(n))) is bounded. Almost sure limit theorems on (log n)(-1) Sigma(n)(k=1) k(-1)I(X-1 <= u(k1), ..., X-k <= u(kk)) and (log n)(-1) Sigma(n)(k=1) k(-1)I(max(1 <= i <= k) X-i <= lambda(k)) are derived.
- 出版日期2011
- 单位西南大学
