Extreme Points of the Convex Set of Joint Probability Distributions with Fixed Marginals
نویسنده
چکیده
By using a quantum probabilistic approach we obtain a description of the extreme points of the convex set of all joint probability distributions on the product of two standard Borel spaces with fixed marginal distributions.
منابع مشابه
On fixed points of fundamentally nonexpansive mappings in Banach spaces
We first obtain some properties of a fundamentally nonexpansive self-mapping on a nonempty subset of a Banach space and next show that if the Banach space is having the Opial condition, then the fixed points set of such a mapping with the convex range is nonempty. In particular, we establish that if the Banach space is uniformly convex, and the range of such a mapping is bounded, closed and con...
متن کاملDetermination of Maximum Bayesian Entropy Probability Distribution
In this paper, we consider the determination methods of maximum entropy multivariate distributions with given prior under the constraints, that the marginal distributions or the marginals and covariance matrix are prescribed. Next, some numerical solutions are considered for the cases of unavailable closed form of solutions. Finally, these methods are illustrated via some numerical examples.
متن کاملOn the Rényi divergence and the joint range of relative entropies
This paper starts with a study of the minimum of the Rényi divergence subject to a fixed (or minimal) value of the total variation distance. Relying on the solution of this minimization problem, we determine the exact region of the points ( D(Q||P1), D(Q||P2) ) where P1 and P2 are any probability distributions whose total variation distance is not below a fixed value, and the probability distri...
متن کاملFixed points for total asymptotically nonexpansive mappings in a new version of bead space
The notion of a bead metric space is defined as a nice generalization of the uniformly convex normed space such as $CAT(0)$ space, where the curvature is bounded from above by zero. In fact, the bead spaces themselves can be considered in particular as natural extensions of convex sets in uniformly convex spaces and normed bead spaces are identical with uniformly convex spaces. In this paper, w...
متن کاملOptimal Transportation with Capacity Constraints
The classical problem of optimal transportation can be formulated as a linear optimization problem on a convex domain: among all joint measures with fixed marginals find the optimal one, where optimality is measured against a cost function. Here we consider a natural but largely unexplored variant of this problem by imposing a pointwise constraint on the joint (absolutely continuous) measures: ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2007