This paper deals with two-stage and multi-stage stochastic programs in which the right-hand sides of the constraints are Gaussian random variables. Such problems are of interest since the use of Gaussian estimators of random variables is widespread. We introduce algorithms to nd upper bounds on the optimal value of two-stage and multi-stage stochastic (minimization) programs with Gaussian right...

The recently introduced correntropy function is an interesting and useful similarity measure between two random variables which has found myriad applications in signal processing. A series expansion for correntropy in terms of higher-order moments of the difference between the two random variables has been used to try to explain its statistical properties for uses such as deconvolution. We exam...

We pose the following extremal conjecture: Let X,Y be jointly Gaussian random variables with linear correlation ρ. For any random variables U, V for which U,X, Y, V form a Markov chain, in that order, we conjecture that: 2−2[I(X;V )+I(Y ;U)] ≥ (1− ρ2)2−2I(U ;V ) + ρ22−2[I(X;U)+I(Y ;V . By letting V be constant, we see that this inequality generalizes a well-known extremal result proved by Ooham...

In this paper a general theory of a random number of random variables is constructed. A description of all random variables ν admitting an analog of the Gaussian distribution under ν-summation, that is, the summation of a random number ν of random terms, is given. The ν-infinitely divisible distributions are described for these ν-summations and finite estimates of the approximation of ν-sum dis...

Conditionally Gaussian random sequences generalize State Space models along two relevant directions: (a) the parameters of the model depend in an arbitrary way from past observations, but once this dependence is realized, the randomness can be expressed in terms of Gaussian random variables, (b) correlation is introduced between the transition and measurement equations, through the presence of ...