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A law of the iterated logarithm for stable summands
| Content Provider | Semantic Scholar |
|---|---|
| Author | Chover, Joshua |
| Copyright Year | 1966 |
| Abstract | That is, the variables (1/\/n)Sn again satisfy E[exp(it(1/Vn)Sn)] =exp(-| t 2), and to achieve a finite lim sup they must be cut down additionally (and multiplicatively) by the factors (2 log log n)-112. For some reason the obvious corresponding statement for the case 7y < 2 does not seem to have been recorded, and it is the purpose of this note to do so. For 0<7y<2, the variables n-<'YSn again satisfy E [exp(itn-ir_Sn)] = exp(t | Y). Since the corresponding distribution function F(x) has tail behavior F(-x) + 1-F(x)(const) I x I -Y as I xI -* oo, instead of exponential decrease as in the 7y = 2 case, we can expect the "cut down factors" to appear otherwise than as multipliers. |
| Starting Page | 441 |
| Ending Page | 443 |
| Page Count | 3 |
| File Format | PDF HTM / HTML |
| Volume Number | 17 |
| Alternate Webpage(s) | http://www.ams.org/journals/proc/1966-017-02/S0002-9939-1966-0189096-2/S0002-9939-1966-0189096-2.pdf |
| Alternate Webpage(s) | https://doi.org/10.1090/S0002-9939-1966-0189096-2 |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
