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Article overview
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On the functional limits for partial sums under stable law | | Khurelbaatar Gonchigdanzan
; Kamil Marcin Kosinski
; | | Date: |
5 Jun 2010 | | Abstract: | For the partial sums $(S_n)$ of independent random variables we define a
stochastic process $s_n(t):=(1/d_n)sum_{k le [nt]} ({S_k}/{k}-mu)$ and prove
that $$(1/{log N})sum_{nle N}(1/n)mathbf {I}igl{s_n(t)le xigr} o
G_t(x)quad ext{a.s.}$$ if and only if $(1/{log N})sum_{nle N}
(1/n)ppigl(s_n(t)le xigr) o G_t(x)$, for some sequence $(d_n)$ and
distribution $G_t$. 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 $alphain (1,2]$. | | Source: | arXiv, 1006.1073 | | Services: | Forum | Review | PDF | Favorites | |
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