Abstract
We present an alternative proof of Sanov’s theorem for Polish spaces in the weak topology that follows via discretization arguments. We combine the simpler version of Sanov’s theorem for discrete finite spaces and well-chosen finite discretizations of the Polish space. The main tool in our proof is an explicit control on the rate of convergence for the approximated measures.
| Original language | English |
|---|---|
| Pages (from-to) | 646-660 |
| Number of pages | 15 |
| Journal | Journal of Theoretical Probability |
| Volume | 36 |
| Issue number | 1 |
| DOIs | |
| State | Published - Mar 2023 |
| Externally published | Yes |
Bibliographical note
Publisher Copyright:© 2022, The Author(s).
Funding
RB is supported by the Mathematical Institute of Leiden University. RIO counted on the support of CNPq, Brazil via a Bolsa de Produtividade em Pesquisa (304475/2019-0) and a Universal Grant (432310/2018-5). GR was partially supported by a Capes/PNPD fellowship 888887.313738/2019-00 while he was a postdoctoral fellow at Federal University of Bahia (UFBA).
| Funders | Funder number |
|---|---|
| Federal University of Bahia | |
| Mathematical Institute of Leiden University | |
| UFBA | |
| Conselho Nacional de Desenvolvimento Científico e Tecnológico | 304475/2019-0, 888887.313738/2019-00, 432310/2018-5 |
Keywords
- Large deviations
- Sanov’s Theorem