Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2023
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2303.15091 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866910288064806912 |
|---|---|
| author | Khachatryan, Linda A. |
| author_facet | Khachatryan, Linda A. |
| contents | The purpose of this note is to recall one remarkable theorem of Khinchin about the special role of the Gaussian distribution. This theorem allows us to give a new interpretation of the Lindeberg condition: it guarantees the uniform integrability of the squares of normed sums of random variables and, thus, the passage to the limit under the expectation sign. The latter provides a simple proof of the central limit theorem for independent random variables. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_15091 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On Khinchin's theorem about the special role of the Gaussian distribution Khachatryan, Linda A. Probability 60F05, 60G50 The purpose of this note is to recall one remarkable theorem of Khinchin about the special role of the Gaussian distribution. This theorem allows us to give a new interpretation of the Lindeberg condition: it guarantees the uniform integrability of the squares of normed sums of random variables and, thus, the passage to the limit under the expectation sign. The latter provides a simple proof of the central limit theorem for independent random variables. |
| title | On Khinchin's theorem about the special role of the Gaussian distribution |
| topic | Probability 60F05, 60G50 |
| url | https://arxiv.org/abs/2303.15091 |