Almost Sure Convergence in Extreme Value Theory
Copyright policy )Almost Sure Convergence in Extreme Value Theory
AbstractLet X1, …, Xn be independent random variables with common distribution function F. Define equation image and let G(x) be one of the extreme‐value distributions. Assume F ∈ D(G), i.e., there exist an> 0 and bn ∈ ℝ such that equation image .Let l(−∞,x)(·) denote the indicator function of the set (−∞,x) and S(G) =: {x : 0 < G(x) < 1}. Obviously, 1(−∞,x)((Mn−bn)/an) does not converge almost surely for any x ∈ S(G). But we shall prove equation image .
- Erasmus University Rotterdam Netherlands
- Peking University China (People's Republic of)
- Peking University China (People's Republic of)
Extreme value theory; extremal stochastic processes, Central limit and other weak theorems, almost sure convergence, arithmetic means, logarithmic means, extreme value distribution
Extreme value theory; extremal stochastic processes, Central limit and other weak theorems, almost sure convergence, arithmetic means, logarithmic means, extreme value distribution
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