| Autor: |
Konstantinos Mamis |
| Jazyk: |
angličtina |
| Rok vydání: |
2022 |
| Předmět: |
|
| Zdroj: |
Examples and Counterexamples, Vol 2, Iss , Pp 100077- (2022) |
| Druh dokumentu: |
article |
| ISSN: |
2666-657X |
| DOI: |
10.1016/j.exco.2022.100077 |
| Popis: |
We extend Stein’s lemma for averages that explicitly contain the Gaussian random variable at a power. We present two proofs for this extension of Stein’s lemma, with the first being a rigorous proof by mathematical induction. The alternative, second proof is a constructive formal derivation in which we express the average not as an integral, but as the action of a pseudodifferential operator defined via the Gaussian moment-generating function. In extended Stein’s lemma, the absolute values of the coefficients of the probabilist’s Hermite polynomials appear, revealing yet another link between Hermite polynomials and normal distribution. |
| Databáze: |
Directory of Open Access Journals |
| Externí odkaz: |
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