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<p>We study the long-time behaviour of matrix-valued stochastic exponentials of Lévy processes, i.e. of multiplicative Lévy processes in the general linear group. In particular, we prove laws of large numbers as well as central limit theorems for the logarithmized norm, logarithmized entries and the logarithmized determinant of the stochastic exponential. Where possible, Berry–Esseen bounds are also stated.</p>

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Limit Theorems for Stochastic Exponentials of Matrix-Valued Lévy Processes

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年6月24日

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  • Anita Behme,
  • Sebastian Mentemeier

摘要

We study the long-time behaviour of matrix-valued stochastic exponentials of Lévy processes, i.e. of multiplicative Lévy processes in the general linear group. In particular, we prove laws of large numbers as well as central limit theorems for the logarithmized norm, logarithmized entries and the logarithmized determinant of the stochastic exponential. Where possible, Berry–Esseen bounds are also stated.