On types of distributions of sums of one class of random power series with independent identically distributed coefficients
By using the method of characteristic functions, we obtain sufficient conditions for the singularity of a random variable. $$ξ = \sum_{k=1}^{∞} 2^{−k}ξ_k,$$ where $ξ_k$ are independent identically distributed random variables taking values $x_0, x_1$, and $x_2$ $(x_0 < x_1 < x_2)$ with...
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| Дата: | 1999 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | Українська Англійська |
| Опубліковано: |
Institute of Mathematics, NAS of Ukraine
1999
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| Онлайн доступ: | https://umj.imath.kiev.ua/index.php/umj/article/view/4591 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
| Завантажити файл: |  |
Репозитарії
Ukrains’kyi Matematychnyi Zhurnal| Резюме: | By using the method of characteristic functions, we obtain sufficient conditions for the singularity of a random variable.
$$ξ = \sum_{k=1}^{∞} 2^{−k}ξ_k,$$
where $ξ_k$ are independent identically distributed random variables taking values $x_0, x_1$, and $x_2$ $(x_0 < x_1 < x_2)$ with probabilities $p_0, p_1$ and $p_2$, respectively, such that $p_i ≥ 0,\; p_0 + p_1 + p_2 = 1$ and $2(x_1 − x_0)/(x_2−x_0)$ is a rational number. |
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