Tight bounds on Poisson tails with applications to Szász-Mirakyan operators
Fuente:
arXiv
Salvato in:
| Autori principali: | , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2025
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866918147201695744 |
|---|---|
| author | Adell, José A. Cárdenas-Morales, Daniel |
| author_facet | Adell, José A. Cárdenas-Morales, Daniel |
| contents | We obtain tight bounds on Poisson tails which are easy to handle. A short proof based on the median of the gamma distribution is given. Numerical comparisons with other known estimates are made. As an application, we consider the rates of pointwise convergence for $S_nf(x)-f(x)$, as $n\rightarrow \infty$, where $S_n$ is the Szász-Mirakyan operator and $x$ belongs to an open interval $I$. If the function $f$ is affine on $I$, the rate of convergence is exponential. This property is no longer true at the boundary of $I$ |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_19935 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Tight bounds on Poisson tails with applications to Szász-Mirakyan operators Adell, José A. Cárdenas-Morales, Daniel Probability 60E05, 41A25 We obtain tight bounds on Poisson tails which are easy to handle. A short proof based on the median of the gamma distribution is given. Numerical comparisons with other known estimates are made. As an application, we consider the rates of pointwise convergence for $S_nf(x)-f(x)$, as $n\rightarrow \infty$, where $S_n$ is the Szász-Mirakyan operator and $x$ belongs to an open interval $I$. If the function $f$ is affine on $I$, the rate of convergence is exponential. This property is no longer true at the boundary of $I$ |
| title | Tight bounds on Poisson tails with applications to Szász-Mirakyan operators |
| topic | Probability 60E05, 41A25 |
| url | https://arxiv.org/abs/2509.19935 |