Inequalities for upper and lower probabilities

Zengjing Chen and Reg Kulperger

Statistics & Probability Letters, 2005, vol. 73, issue 3, 233-241

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.

Keywords: Multiple; priors; 2-alternating; Backward; stochastic; differential; equation; (BSDE) (search for similar items in EconPapers)
Date: 2005
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