On the functional limits for partial sums under stable law
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| Publication date | 2009 |
| Journal | Statistics & Probability Letters |
| Volume | Issue number | 79 | 17 |
| Pages (from-to) | 1818-1822 |
| Organisations |
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| Abstract | For the partial sums (S,) of independent random variables we define a stochastic process s(n)(t) := (1/d(n)) Sigma(k <=[nt])(S-k/k - mu) and prove that (1/log N) Sigma(n <= N)(1/n)I {S-n(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 alpha-stable law with alpha is an element of (1, 2). |
| Document type | Article |
| Published at |
https://doi.org/10.1016/j.spl.2009.05.004
(Final published version)
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