On the Lebesgue structure of the distribution of a random variable defined by continued $A_2$-fractions
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866912167300694016 |
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| author | Mykola, Pratsiovytyi Oleg, Makarchuk Dmytro, Karvatskyi |
| author_facet | Mykola, Pratsiovytyi Oleg, Makarchuk Dmytro, Karvatskyi |
| contents | In this paper, we study the Lebesgue structure of the distribution of a random variable given in terms of a continued fraction with a two-symbol alphabet $\{\frac{1}{2}, 1\}$, also known as $A_2$-fractions. We establish necessary and sufficient conditions for the distribution to be discrete and provide some sufficient conditions for its singularity. We also explore non-trivial metric properties of the $A_2$-representation with the specified alphabet. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_17430 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the Lebesgue structure of the distribution of a random variable defined by continued $A_2$-fractions Mykola, Pratsiovytyi Oleg, Makarchuk Dmytro, Karvatskyi Probability 60E05 In this paper, we study the Lebesgue structure of the distribution of a random variable given in terms of a continued fraction with a two-symbol alphabet $\{\frac{1}{2}, 1\}$, also known as $A_2$-fractions. We establish necessary and sufficient conditions for the distribution to be discrete and provide some sufficient conditions for its singularity. We also explore non-trivial metric properties of the $A_2$-representation with the specified alphabet. |
| title | On the Lebesgue structure of the distribution of a random variable defined by continued $A_2$-fractions |
| topic | Probability 60E05 |
| url | https://arxiv.org/abs/2412.17430 |