منابع مشابه
Partitioning General Probability Measures'
Georgia Institute of Technology Suppose l,..., An are probability measures on the same measurable space (2, Y). Then if all atoms of each Ai have mass a or less, there is a measurable partition Al,..., An of 2 so that pxi(Ai) 2 Vn(a) for all i = 1, ..., n, where Vn(.) is an explicitly given piecewise linear nonincreasing continuous function on [0,1]. Moreover, the bound Vn(a) is attained for al...
متن کاملPartitioning General Probability Measures' by Theodore
Georgia Institute of Technology Suppose l,..., An are probability measures on the same measurable space (2, Y). Then if all atoms of each Ai have mass a or less, there is a measurable partition Al,..., An of 2 so that pxi(Ai) 2 Vn(a) for all i = 1, ..., n, where Vn(.) is an explicitly given piecewise linear nonincreasing continuous function on [0,1]. Moreover, the bound Vn(a) is attained for al...
متن کاملOptimal-partitioning Inequalities for Nonatomic Probability Measures
Suppose fix,... ,fin are nonatomic probability measures on the same measurable space (S, S). Then there exists a measurable partition isi}"=i of 5 such that Pi(Si) > (n + 1 M)'1 for a11 i l,...,n, where M is the total mass of V?=i ßi (tne smallest measure majorizing each m). This inequality is the best possible for the functional M, and sharpens and quantifies a well-known cake-cutting theorem ...
متن کاملCoherent Risk Measures on General Probability Spaces
We extend the definition of coherent risk measures, as introduced by Artzner, Delbaen, Eber and Heath, to general probability spaces and we show how to define such measures on the space of all random variables. We also give examples that relates the theory of coherent risk measures to game theory and to distorted probability measures. The mathematics are based on the characterisation of closed ...
متن کاملA General Classification Rule for Probability Measures 1
We consider the problem of classifying an unknown probability distribution based on a sequence of random samples drawn according to this distribution. Specifically, if A is a subset of the space of all probability measures M1(E) over some compact Polish space E, we want to decide whether or not the unknown distribution belongs to A or its complement. We propose an algorithm which leads a.s. to ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: The Annals of Probability
سال: 1987
ISSN: 0091-1798
DOI: 10.1214/aop/1176992173