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- Publisher
- Springer Basel
- Copyright
- © Springer Basel 2013
- ISBN
- 978-3-0348-0489-9
- Pages
- 19 –53
- DOI
- 10.1007/978-3-0348-0490-5_2
- Publisher site
- See Chapter on Publisher Site
Abstract
[Slepian’s inequality comes in many variants under different sets of regularity conditions. Unfortunately, some of these variants are wrong and other variants are imposing to strong regularity conditions. The first part of this paper contains a unified version of Slepian’s inequality under minimal regularity conditions, covering all the variants I know about. It is well known that Slepian’s inequality is closely connected to integral orderings in general and the supermodular ordering in particular. In the last part of the paper I explore this connection and corrects some results in the theory of integral orderings.]
Published: Apr 1, 2013
Keywords: Integral orderings; modular functions; Gaussian vectors