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Abstract <p>We consider semi-invariants (or cumulants), which are an alternative characteristic to moments when studying the properties of certain distributions (examples of studying such distributions, as well as the motivation for studying exactly these characteristics of distributions are presented in the paper of Leonov and Shiryaev (1959). As an example of the transition to semi-invariants, the moment problem is provided. While we deal with this problem, the question arises: what is the criteria for the solution to this problem to be unique. The uniqueness of the problem can be studied and the problem can be reformulated in terms of semi-invariants. These conditions, in turn, are used to prove limit theorems.</p>

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Sufficient Solvability Conditions of the Moment Problem in Terms of Semi-Invariants

  • 期刊论文

  • 发表日期：

    2025年6月1日

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  • K. K. Kostyashin

摘要

Abstract

We consider semi-invariants (or cumulants), which are an alternative characteristic to moments when studying the properties of certain distributions (examples of studying such distributions, as well as the motivation for studying exactly these characteristics of distributions are presented in the paper of Leonov and Shiryaev (1959). As an example of the transition to semi-invariants, the moment problem is provided. While we deal with this problem, the question arises: what is the criteria for the solution to this problem to be unique. The uniqueness of the problem can be studied and the problem can be reformulated in terms of semi-invariants. These conditions, in turn, are used to prove limit theorems.