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• W2667989023 abstract "Abstract An rth-order extremal process Δ ( r ) = (Δ ( r ) t ) t ≥0 is a continuous-time analogue of the r th partial maximum sequence of a sequence of independent and identically distributed random variables. Studying maxima in continuous time gives rise to the notion of limiting properties of Δ t ( r ) as t ↓ 0. Here we describe aspects of the small-time behaviour of Δ ( r ) by characterising its upper and lower classes relative to a nonstochastic nondecreasing function b t > 0 with lim t ↓ b t = 0. We are then able to give an integral criterion for the almost sure relative stability of Δ t ( r ) as t ↓ 0, r = 1, 2, . . ., or, equivalently, as it turns out, for the almost sure relative stability of Δ t (1) as t ↓ 0." @default.
• W2667989023 created "2017-06-30" @default.
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• W2667989023 date "2017-06-01" @default.
• W2667989023 modified "2023-10-18" @default.
• W2667989023 title "Small-time almost-sure behaviour of extremal processes" @default.
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• W2667989023 doi "https://doi.org/10.1017/apr.2017.7" @default.
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