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On the almost sure central limit theorem for self-normalized products of partial sums ofϕ-mixing random variables

✍ Scribed by Kyo-Shin Hwang

Book ID: 120732621
Publisher: Hindawi Publishing Corporation
Year: 2013
Tongue: English
Weight: 233 KB
Volume: 2013
Category: Article
ISSN: 1025-5834
DOI: 10.1186/1029-242X-2013-155

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We give conditions under which the self-normalized product of independent and identically distributed (i.i.d) random variables X1; X2; : : :, where \* denotes the sum over all n-1-long sequences of integers 16i1¡i2¡ • • • ¡in-16n, is asymptotically normally distributed as n → ∞.