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VIDEO LIBRARY |
Complex Analysis and Related Topics (satelllite of ICM-2022)
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Limit distribution for compositions of random operators V. Zh. Sakbaev, E. V. Shmidt |
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Abstract: Limit theorems for compositions of independent linear operators acting in a finite dimensional Euclidean space It is known (see [1]) that the limit properties of distribution of the sum of random variables with values in the topological vector spaces can be described by limit theorems. In particular, the law of large numbers describes the convergence in probability of the sequence of averaged sum of independent identically distributed (iid) random vector valued variables to the limit of the mean value of the sum. The central limit theorem gives the conditions of the convergence in distribution for the sequence of averaged sum of iid random vector valued variables to the Gaussian random vector. We study the sequence of compositions of iid random variables with values in the Banach algebra of bounded linear operators Language: English References
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