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.

中文翻译：

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随机算子测度和极限定理弱收敛的算子法

摘要

度量序列的广义弱收敛是由度量生成的线性算子的收敛引起的。引入了分布收敛概念的相应推广。研究了独立随机变换的组合序列分布上的广义收敛性。建立了求解演化方程初边值问题的极限分布和半群之间的联系。在向欧几里得空间的随机向量的移位的独立随机变换的组合序列的情况下，获得的结果与独立随机向量之和的中心极限定理一致。