Question: MJ (t) M(t) if t < 1. [You may use the fact that J t(J t)/(J ) 1 as J .] It follows

MJ (t)→ M(t) if t < 1.

[You may use the fact that J tŴ(J − t)/Ŵ(J )→ 1 as J → ∞.] It follows that the distribution of UJ approaches the extreme-value distribution as J → ∞.

202 Random processes in continuous time

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