Lévy's probability measures on Euclidean spaces

Coherent 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 ...

Composition of Probability Measures on Finite Spaces

Decomposable models and Bayesian net­ works can be defined as sequences of oligo­ dimensional probability measures connected with opemtors of composition. The prelim­ inary results suggest that the probabilistic models allowing for effective computational procedures are represented by sequences pos­ sessing a special property; we shall call them perfect sequences. The present paper lays down th...

Kullback-Leibler Approximation for Probability Measures on Infinite Dimensional Spaces

In a variety of applications it is important to extract information from a probability measure μ on an infinite dimensional space. Examples include the Bayesian approach to inverse problems and (possibly conditioned) continuous time Markov processes. It may then be of interest to find a measure ν, from within a simple class of measures, which approximates μ. This problem is studied in the case ...

On quasiplanes in Euclidean spaces

A variational inequality for the images of k-dimensional hyper-planes under quasiconformal maps of the n-dimensional Euclidean space is proved when 1 ≤ k ≤ n − 2 .

On Isometries of Euclidean Spaces