Limit theorems for stochastic exponentials of matrix-valued Lévy processes

Fuente: arXiv
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Main Authors: Behme, Anita, Mentemeier, Sebastian
Format: Preprint
Published: 2024
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author Behme, Anita
Mentemeier, Sebastian
author_facet Behme, Anita
Mentemeier, Sebastian
contents 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 logarithmised norm, logarithmised entries and the logarithmised determinant of the stochastic exponential. Where possible, also Berry-Esseen bounds are stated.
format Preprint
id arxiv_https___arxiv_org_abs_2411_14876
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Limit theorems for stochastic exponentials of matrix-valued Lévy processes
Behme, Anita
Mentemeier, Sebastian
Probability
60G51, 60J57 (primary), 60H10, 60B15 (secondary)
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 logarithmised norm, logarithmised entries and the logarithmised determinant of the stochastic exponential. Where possible, also Berry-Esseen bounds are stated.
title Limit theorems for stochastic exponentials of matrix-valued Lévy processes
topic Probability
60G51, 60J57 (primary), 60H10, 60B15 (secondary)
url https://arxiv.org/abs/2411.14876