Extended covariance identities and inequalities
β Scribed by Nicolas Privault
- Book ID
- 104301756
- Publisher
- Elsevier Science
- Year
- 2001
- Tongue
- English
- Weight
- 116 KB
- Volume
- 55
- Category
- Article
- ISSN
- 0167-7152
No coin nor oath required. For personal study only.
β¦ Synopsis
We state an abstract version of covariance identities and inequalities for normal martingales, which uses any gradient operator that satisΓΏes a Clark formula. This extends and makes more precise some results of HoudrΓ e and PΓ erez-Abreu (Ann. Probab. 23 (1995)), with simpliΓΏed proofs.
π SIMILAR VOLUMES
We introduce some identities for the derivative of a trigonometric polynomial which are obtained from the identity of Riesz. We then use these new identities to derive some inequalities for derivatives of trigonometric and algebraic polynomials. Among our results are a weighted \(L^{p}\) inequality
We give pseudo-LYM inequalities in some posets and we give a new restriction in this way for their antichains. Typically these posets fail the LYM inequality and some of them are known to not be Sperner.