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| Hlavní autor: | |
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| Médium: | Preprint |
| Vydáno: |
2024
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| Témata: | |
| On-line přístup: | https://arxiv.org/abs/2404.03513 |
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Obsah:
- A convenient framework for dealing with asymptotic limit problems of probabilistic nature is provided. These problems include questions such as finding the asymptotic proportion of terms of a sequence falling inside a given interval, or the limit of the arithmetic mean of its partial sums; but several classes of problems are examined in a much more general setting. The proposed framework, which aims to unify those questions and their solution, is based on the idea that to any finite multiset $E_n$, one can associate a finitely distributed atomic probability $μ_n$; assuming $μ_n$ tends in distribution to a probability $μ$, it provides the tools needed to establish the desired asymptotic limit. Few examples are worked out in order to illustrate how using the framework.