We consider a random variable X satisfying almost-sure conditions involving G := DX; DL X where DX is X’s Malliavin derivative and L 1 is the pseudo-inverse of the generator of the OrnsteinUhlenbeck semigroup. A lower(resp. upper-) bound condition on G is proved to imply a Gaussian-type lower (resp. upper) bound on the tail P [X > z]. Bounds of other natures are also given. A key ingredient is ...

We consider a nearest-neighbor, one-dimensional random walk {Xn}n≥0 in a random i.i.d. environment, in the regime where the walk is transient with speed vP > 0 and there exists an s ∈ (1,2) such that the annealed law of n−1/s(Xn − nvP ) converges to a stable law of parameter s. Under the quenched law (i.e., conditioned on the environment), we show that no limit laws are possible. In particular ...

High Order Statistics (HOS) are widely used in many algorithms ranging from blind identification to signal separation. A well-known identifiability result is that at most one Gaussian source should be present in static mixtures [J. Eriksson, V. Koivunen, Identifiability, separability and uniqueness of linear ICA models, IEEE Signal Process. Lett. (2004) 601–604]. The reason for this is that the...

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...

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...