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- W2897528315 abstract "Let ${X_{mathbf{n}} : mathbf{n}inmathbb{Z}^d}$ be a weakly dependent stationary field with maxima $M_{A} := sup{X_{mathbf{i}} : mathbf{i}in A}$ for finite $Asubsetmathbb{Z}^d$ and $M_{mathbf{n}} := sup{X_{mathbf{i}} : mathbf{1} leq mathbf{i} leq mathbf{n} }$ for $mathbf{n}inmathbb{N}^d$. In a general setting we prove that $P(M_{(n,n,ldots, n)} leq v_n) = exp(- n^d P(X_{mathbf{0}} > v_n , M_{A_n} leq v_n)) + o(1)$, for some increasing sequence of sets $A_n$ of size $ o(n^d)$. For a class of fields satisfying a local mixing condition, including $m$-dependent ones, the theorem holds with a constant finite $A$ replacing $A_n$. The above results lead to new formulas for the extremal index for random fields." @default.
- W2897528315 created "2018-10-26" @default.
- W2897528315 creator A5017472451 @default.
- W2897528315 date "2018-10-10" @default.
- W2897528315 modified "2023-09-27" @default.
- W2897528315 title "On maxima of stationary fields" @default.
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- W2897528315 hasPublicationYear "2018" @default.
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