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On the functional limits for partial sums under stable law

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Author Info
Gonchigdanzan, Khurelbaatar
Kosinski, Kamil M.
Abstract

For the partial sums (Sn) of independent random variables we define a stochastic process sn(t):=(1/dn)[summation operator]k<=[nt](Sk/k-[mu]) and prove that a.s. if and only if , for some sequence (dn) and distribution Gt. We also prove an almost sure functional limit theorem for the product of partial sums of i.i.d. positive random variables attracted to an [alpha]-stable law with [alpha][set membership, variant](1,2].

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Article provided by Elsevier in its journal Statistics & Probability Letters.

Volume (Year): 79 (2009)
Issue (Month): 17 (September)
Pages: 1818-1822
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Handle: RePEc:eee:stapro:v:79:y:2009:i:17:p:1818-1822

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This page was last updated on 2009-12-3.

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