Abstract
The generalized weak convergence of a sequence of measures is induced by the convergence of the linear operators generated by the measures. A corresponding generalization of the notion of convergence over a distribution is introduced. Generalized convergence over the distribution of a sequence of compositions of independent random transformations is investigated. The connection between limit distributions and semigroups that solve initial-boundary value problems for evolution equations is established. In the case of a sequence of compositions of independent random transformations of the shift to a random vector of Euclidean space, the results obtained coincide with the central limit theorem for sums of independent random vectors.
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Orlov, Y.N., Sakbaev, V.Z. & Shmidt, E.V. Operator Approach to Weak Convergence of Measures and Limit Theorems for Random Operators. Lobachevskii J Math 42, 2413–2426 (2021). https://doi.org/10.1134/S1995080221100188
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DOI: https://doi.org/10.1134/S1995080221100188