Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
10525876 | Statistics & Probability Letters | 2005 | 9 Pages |
Abstract
An upper (lower) probability can be defined as a supremum (infimum) over a set of probability measures. The upper probability measure is also called a capacity. A capacity is usually studied under an assumption that it is 2-alternating, but many capacities are not 2-alternating. In this paper, we introduce a new definition of sub 2-alternating, defined for a capacity and its conjugate capacity. We study these inequalities for a certain natural capacity that is the supremum over a particular set of probability measures with a particular form of Radon Nikodym derivative with respect to Brownian motion. This capacity is not 2-alternating, but the pair of the capacity and its conjugate capacity is sub 2-alternating.
Related Topics
Physical Sciences and Engineering
Mathematics
Statistics and Probability
Authors
Zengjing Chen, Reg Kulperger,