9 11 Apply the first BorelCantelli lemma 1 28 to the events An ln (1 ) log2 n Conclude that for each 0, with probability 1, ln (1 ) log2 n for all n large enough Take a countable sequence k 0, and then conclude that lim sup n Ln log2 n 1, a s ...

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9.11 Apply the first BorelCantelli lemma 1.28 to the events An = {ln > (1 + )

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9.11 Apply the first Borel–Cantelli lemma 1.28 to the events An = {ln > (1 + ε) log2 n}.

Conclude that for each ε > 0, with probability 1, ln ≤ (1 + ε) log2 n for all n large enough.

Take a countable sequence εk ↓ 0, and then conclude that lim sup n→∞

Ln log2 n

≤ 1, a.s.

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Probability And Stochastic Processes

ISBN: 9780470624555

1st Edition

Authors: Ionut Florescu

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Question Posted: Nov 05, 2024 08:00 AM

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9.11 Apply the first BorelCantelli lemma 1.28 to the events An = {ln > (1 + )

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Probability And Stochastic Processes

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