Question: 1.15. Generalize Theorem 8.3.3 to (!Il2 as follows. If the central limit theorem applies in the fonn that Sn I .Jli converges in dist. to

1.15. Generalize Theorem 8.3.3 to (!Il2 as follows. If the central limit theorem applies in the fonn that Sn I .Jli converges in dist. to the unit nonnal, then the random walk is recurrent. [HINT: Use ExercIses I3 and 14 and Exercise 4 of § 4 3 This is sharper than Exercise 11 No proof of Exercise 12 using a similar method is known.]

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