Abstract
For normalized sums Zn of i.i.d. random variables, we explore necessary and sufficient conditions, which guarantee the normal approximation with respect to the Rényi divergence of infinite order. In terms of densities pn of Zn, this is a strengthened variant of the local limit theorem taking the form (Formula presented) as n → ∞.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 453-477 |
| Number of pages | 25 |
| Journal | Annals of Probability |
| Volume | 53 |
| Issue number | 2 |
| DOIs | |
| State | Published - 2025 |
Bibliographical note
Publisher Copyright:© Institute of Mathematical Statistics, 2025
Keywords
- Central limit theorem
- Rényi divergence
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