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- W60983802 abstract "$(m_{n}-b_{n})/a_{n}$ has a nondegenerate limit distribution then the sequence ${M_{n}, ngeq 1}$ of random functions $M_{n}$ defined by $M_{n}(t)=(m_{[nt]}-b_{n})/a_{n}$ , each $M_{n}$ being considered as an element of the space $D[a,$ $ b1,0<a<b<infty$ , of nondecreasing right-continuous functions endowed with the Skorohod $J_{1}$ topology, converges in distribution to an extremal process. Recently Resnik [91, Mori and Oodaira [8] considered point process $Phi_{n}$ on $R^{2}$ consisting of random points $(k/n, (xi_{k}-b_{n})/a_{n}),$ $kgeq 1$ . They showed that if $xi_{n}s$ are i.i. $d$ . and if $(m_{n}-b_{n})/a_{n}$ has a nondegenerate limit distribution then $Phi_{n}$ converges to a Poisson point process. Weissman $[10, 11]$ used this approach to nonidentically distributed $xi_{n}s$ . When ${xi_{n}}$ is a stationary strong-mixing sequence Loynes [5] proved that the only possible limit laws for $(m_{n}-b_{n})/a_{n}$ are the same types that occur in the independent case. Welsch [12] showed that the class of possible limit laws of" @default.
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- W60983802 date "1977-01-01" @default.
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- W60983802 title "LIMIT DISTRIBUTIONS OF TWO-DIMENSIONAL POINT PROCESSES GENERATED BY STRONG-MIXING SEQUENCES" @default.
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