| Autor: |
Iksanov, Alexander, Kotelnikova, Valeriya |
| Předmět: |
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| Zdroj: |
Modern Stochastics: Theory & Applications; Mar2024, Vol. 11 Issue 2, p217-245, 29p |
| Abstrakt: |
In the Karlin infinite occupancy scheme, balls are thrown independently into an infinite array of boxes 1, 2, ..., with probability pk of hitting the box k. For j, n ∈ N, denote by Kj* (n) the number of boxes containing exactly j balls provided that n balls have been thrown. Small counts are the variables Kj* (n), with j fixed. The main result is a law of the iterated logarithm (LIL) for the small counts as the number of balls thrown becomes large. Its proof exploits a Poissonization technique and is based on a new LIL for infinite sums of independent indicators ... where the family of events (Ak(t))t≥0 is not necessarily monotone in t . The latter LIL is an extension of a LIL obtained recently by Buraczewski, Iksanov and Kotelnikova (2023+) in the situation when (Ak(t))t≥0 forms a nondecreasing family of events. [ABSTRACT FROM AUTHOR] |
| Databáze: |
Complementary Index |
| Externí odkaz: |
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