Distributions with given Marginals and Moment Problems, 1997

The last decade has seen a remarkable development of the "Marginal and Moment Problems" as a research area in Probability and Statistics. Its attractiveness stemmed from its lasting ability to provide a researcher with difficult theoretical problems that have direct consequences for appli­ cations outside of mathematics. The relevant research aims centered mainly along the following lines that very frequently met each other to provide sur­ prizing and useful results : -To construct a probability distribution (to prove its existence, at least) with a given support and with some additional inner stochastic property defined typically either by moments or by marginal distributions. -To study the geometrical and topological structure of the set of prob­ ability distributions generated by such a property mostly with the aim to propose a procedure that would result in a stochastic model with some optimal properties within the set of probability distributions. These research aims characterize also, though only very generally, the scientific program of the 1996 conference "Distributions with given marginals and moment problems" held at the beginning of September in Prague, Czech Republic, to perpetuate the tradition and achievements of the closely related 1990 Roma symposium "On Frechet Classes" 1 and 1993 Seattle" AMS Summer Conference on Marginal Problem".

Optimal bounds on the average of a rounded off observation in the presence of a single moment condition.- The complete solution of a rounding problem under two moment conditions.- Methods of realization of moment problems with entropy maximization.- Matrices of higher moments: some problems of representation.- The method of moments in tomography and quantum mechanics.- Moment problems in stochastic geometry.- Fréchet classes and nonmonotone dependence.- Comonotonicity, rank-dependent utilities and a search problem.- A stochastic ordering based on a decomposition of Kendall’s tau.- Maximum entropy distributions with prescribed marginals and normal score correlations.- On bivariate distributions with Polya-Aeppli or Lüders-Delaporte marginals.- Boundary distributions with fixed marginals.- On approximations of copulas.- Joint distributions of two uniform random variables when the sum and difference are independent.- Diagonal copulas.- Copulas constructed from diagonal sections.- Continuous scaling on a bivariate copula.- Representation of Markov kernels by random mappings under order conditions.- How to construct a two dimensional random vector with a given conditional structure.- Strassen’s theorem for group-valued charges.- The Lancaster’s probabilities on R2 and their extreme points.- On marginalization, collapsibility and precollapsibility.- Moment bounds for stochastic programs in particular for recourse problems.- Probabilistic constrained programming and distributions with given marginals.- On an ?-solution of minimax problem in stochastic programming.- Bounds for stochastic programs — nonconvex case.- Artificial intelligence, the marginal problem and inconsistency.- Inconsistent marginal problem on finite sets.- Topics in the duality for mass transferproblems.- Generalising monotonicity.- On optimal multivariate couplings.- Optimal couplings between one-dimensional distributions.- Duality theorems for assignments with upper bounds.- Bounding the moments of an order statistics if each k-tuple is independent.

This volume contains the Proceedings of the 1996 Prague Conference on `Distributions with Given Marginals and Moment Problems'. It provides researchers with difficult theoretical problems that have direct consequences for applications outside mathematics. Contributions centre around the following two main themes. Firstly, an attempt is made to construct a probability distribution, or at least prove its existence, with a given support and with some additional inner stochastic property defined typically either by moments or by marginal distributions. Secondly, the geometrical and topological structures of the set of probability distributions generated by such a property are studied, mostly with the aim to propose a procedure that would result in a stochastic model with some optimal propertie