Свойство RUC для хаоса случайных величин в равномерной норме
EDN: RXOTNQ
Аннотация
Пусть $X=\{X_k\}_{k=1}^\infty$ – последовательность независимых симметричных и ограниченных случайных величин. В работе рассматриваются системы вида $\{X_iX_j\}_{i<j}$, $\{X_i X_j X_k\}_{i<j<k},\ldots$, конечные объединения таких систем и близкие к ним системы в пространстве $L_\infty$ ограниченных случайных величин. Ряды по таким системам не обладают свойством безусловности: сходимость рядов зависит от порядка, в котором нумеруются элементы системы. В то же время, как показано в работе, такие системы обладают очень бизким свойством случайной безусловной сходимости.}
Об авторах
П. А. Слиняков
Институт математики НАН Беларуси; Белорусский государственный университет
Беларусь
Беларусь
Минск
К. В. Лыков
Институт математики НАН Беларуси; Белорусский государственный университет
Беларусь
Беларусь
Минск
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Рецензия
Для цитирования:
Слиняков П.А., Лыков К.В. Свойство RUC для хаоса случайных величин в равномерной норме. Труды Института математики НАН Беларуси. 2025;33(2):54-72. EDN: RXOTNQ
For citation:
Slinyakov P.A., Lykov K.V. RUC property for chaos of random variables in the uniform norm. Proceedings of the Institute of Mathematics of the NAS of Belarus. 2025;33(2):54-72. EDN: RXOTNQ
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