The integral representation ring $a(R\sb{k}G)$

The bipolar Choquet integral representation

Cumulative Prospect Theory of Tversky and Kahneman (1992) is the modern version of Prospect Theory (Kahneman and Tversky (1979)) and is nowadays considered a valid alternative to the classical Expected Utility Theory. Cumulative Prospect theory implies Gain-Loss Separability, i.e. the separate evaluation of losses and gains within a mixed gamble. Recently, some authors have questioned this assu...

Integral Representation without Additivity

Let J be a norm-continuous functional on the space B of bounded E-measurable real valued functions on a set S, where S is an algebra of subsets of S. Define a set function v on £ by : v(E) equals the value of I at the indicator function of E. For each a in B let /0 coo (v(a > a) v(S)) da+ v(a > a) da. -oo Jo Then / = J on B if and only if I(b + c) = 1(b) + 1(c) whenever (b(s) b(t))(c(s) c(t)) >...

Integral representation of the Drazin inverse

Integral Representation of the Error and AsymptoticError

In this paper we will give an integral representation of the error for the generalized Pad e type approximants deened in 2]. We will deduce some asymptotic upper bounds on the error of sequences of these approximants. As applications, we will consider functions deened by their expansions in some families of classical orthogonal polynomials and obtain for the corresponding approximants some resu...

An Integral Representation of the Relative Entropy

Recently the identity of de Bruijn type between the relative entropy and the relative Fisher information with the reference moving has been unveiled by Verdú via MMSE in estimation theory. In this paper, we shall give another proof of this identity in more direct way that the derivative is calculated by applying integrations by part with the heat equation. We shall also derive an integral repre...