Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2501.16963 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866929689839271936 |
|---|---|
| author | Shmyrov, Alexander Shmyrov, Vasily |
| author_facet | Shmyrov, Alexander Shmyrov, Vasily |
| contents | A non-classical formulation of the central limit theorem is given for sequences of independent random variables with finite second moments. Singular sequences whose members all have a degenerate or normal distribution are excluded from consideration. The condition of uniform convergence is imposed on the improper integrals defining the variances. Under the conditions of non-singularity and uniform convergence, the central limit theorem is valid if and only if the total variance increases indefinitely. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_16963 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On a formulation of the central limit theorem Shmyrov, Alexander Shmyrov, Vasily Probability 60F05 G.3 A non-classical formulation of the central limit theorem is given for sequences of independent random variables with finite second moments. Singular sequences whose members all have a degenerate or normal distribution are excluded from consideration. The condition of uniform convergence is imposed on the improper integrals defining the variances. Under the conditions of non-singularity and uniform convergence, the central limit theorem is valid if and only if the total variance increases indefinitely. |
| title | On a formulation of the central limit theorem |
| topic | Probability 60F05 G.3 |
| url | https://arxiv.org/abs/2501.16963 |