We analyze the Gaussian approximation as a method to obtain the first and second moments of a stochastic process described by a master equation. We justify the use of this approximation with ideas coming from van Kampen’s expansion approach (the fact that the probability distribution is Gaussian at first order). We analyze the scaling of the error with a large parameter of the system and compar...

We study the maximal mutual information about a random variable Y (representing non-private information) displayed through an additive Gaussian channel when guaranteeing that only ε bits of information is leaked about a random variable X (representing private information) that is correlated with Y . Denoting this quantity by gε(X,Y ), we show that for perfect privacy, i.e., ε = 0, one has g0(X,...

In this paper we propose a class of 2D circularly-symmetric filter banks based on a 1D IIR Gaussian prototype. We approach two cases, namely dyadic and uniform filter banks. The Gaussian prototype is obtained using an efficient rational approximation, namely the Chebyshev-Padé approximation. Then, using a frequency transformation, the corresponding 2D filters with circular symmetry are derived....