 Author
 Year
 2009
 Title
 On the functional limits for partial sums under stable law
 Journal
 Statistics & Probability Letters
 Volume  Issue number
 79  17
 Pages (fromto)
 18181822
 Document type
 Article
 Faculty
 Faculty of Science (FNWI)
 Institute
 Kortewegde Vries Institute for Mathematics (KdVI)
 Abstract

For the partial sums (S,) of independent random variables we define a stochastic process s(n)(t) := (1/d(n)) Sigma(k <=[nt])(Sk/k  mu) and prove that (1/log N) Sigma(n <= N)(1/n)I {Sn(t) <= x} > G(t)(x) a.s. if and only if (1/log N) Sigma(n <= N)(1/n)P(s(n)(t) <= x) > 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 alphastable law with alpha is an element of (1, 2).
 URL
 go to publisher's site
 Language
 Undefined/Unknown
 Permalink
 http://hdl.handle.net/11245/1.315201
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