Limit theorems for stochastic exponentials of matrix-valued Lévy processes
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866913583532605440 |
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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 |