A Framework for Asymptotic Limit Problems of Probabilistic Nature
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866910399162482688 |
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| author | Bensimhoun, Michaël |
| author_facet | Bensimhoun, Michaël |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_03513 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Framework for Asymptotic Limit Problems of Probabilistic Nature Bensimhoun, Michaël History and Overview Probability 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. |
| title | A Framework for Asymptotic Limit Problems of Probabilistic Nature |
| topic | History and Overview Probability |
| url | https://arxiv.org/abs/2404.03513 |