|
| | | | |
| | | |
| Stat |
Members: 3645
Articles: 2'501'711
Articles rated: 2609
20 April 2024 |
|
| | | | |
|
Article overview
| |
|
|
Algebraic methods toward higher-order probability inequalities, II | | Donald St. P. Richards
; | | Date: |
6 Oct 2004 | | Journal: | Annals of Probability 2004, Vol. 32, No. 2, 1509-1544 DOI: 10.1214/009117904000000298 | | Subject: | Probability MSC-class: 60E15 (Primary) 60J60. (Secondary) | math.PR | | Abstract: | Let (L,preccurlyeq) be a finite distributive lattice, and suppose that the functions f_1,f_2:L o R are monotone increasing with respect to the partial order preccurlyeq. Given mu a probability measure on L, denote by E(f_i) the average of f_i over L with respect to mu, i=1,2. Then the FKG inequality provides a condition on the measure mu under which the covariance, Cov(f_1,f_2):=E(f_1f_2)-E(f_1)E(f_2), is nonnegative. In this paper we derive a ``third-order’’ generalization of the FKG inequality. We also establish fourth- and fifth-order generalizations of the FKG inequality and formulate a conjecture for a general mth-order generalization. For functions and measures on R^n we establish these inequalities by extending the method of diffusion processes. We provide several applications of the third-order inequality, generalizing earlier applications of the FKG inequality. Finally, we remark on some connections between the theory of total positivity and the existence of inequalities of FKG-type within the context of Riemannian manifolds. | | Source: | arXiv, math.PR/0410155 | | Services: | Forum | Review | PDF | Favorites | |
|
|
No review found.
Did you like this article?
Note: answers to reviews or questions about the article must be posted in the forum section.
Authors are not allowed to review their own article. They can use the forum section.
browser Mozilla/5.0 AppleWebKit/537.36 (KHTML, like Gecko; compatible; ClaudeBot/1.0; +claudebot@anthropic.com)
|
| |
|
|
|
|
News, job offers and information for researchers and scientists:
| |
REGISTER