Erratum to: Convex Ordering for Random Vectors Using Predictable Representation

Convex ordering for random vectors using predictable representation

We prove convex ordering results for random vectors admitting a predictable representation in terms of a Brownian motion and a non-necessarily independent jump component. Our method uses forward-backward stochastic calculus and extends the results proved in [4] in the one-dimensional case. We also study a geometric interpretation of convex ordering for discrete measures in connection with the c...

Ellipsoid Approximation Using Random Vectors

We analyze the behavior of a random matrix with independent rows, each distributed according to the same probability measure on R or on 2. We investigate the spectrum of such a matrix and the way the ellipsoid generated by it approximates the covariance structure of the underlying measure. As an application, we provide estimates on the deviation of the spectrum of Gram matrices from the spectru...

Autoregressive Gaussian Random Vectors of First Order

Attacking Predictable IPsec ESP Initialization Vectors

Predictable initialization vectors in IPsec ESP encryption, allowed by the IPsec specifications and used by most implementations, compromise IPsec confidentiality. By using an adaptive chosen plaintext attack, an attacker can break low entropy plaintext blocks using brute force, and confirm guesses of the contents of arbitrary plaintext blocks. We analyze the preconditions and the seriousness o...

Admissible Vectors of a Covariant Representation of a Dynamical System

In this paper, we introduce admissible vectors of covariant representations of a dynamical system which are extensions of the usual ones, and compare them with each other. Also, we give some sufficient conditions for a vector to be admissible vector of a covariant pair of a dynamical system.  In addition, we show the existence of Parseval frames for some special subspaces of $L^2(G)$ related to...