We study here the elementary properties of the relative entropyH(A,B) = Tr[φ(A)−φ(B)−φ(B)(A−B)] for φ a convex function and A,B bounded self-adjoint operators. In particular, we prove that this relative entropy is monotone if and only if φ is operator monotone. We use this to appropriately define H(A,B) in infinite dimension. In this paper we introduce a relative entropy H(A,B) of two bounded o...

We introduce an axiomatic approach to entropies and relative that relies only on minimal information-theoretic axioms, namely monotonicity under mixing data-processing as well additivity for product distributions. find these axioms induce sufficient structure establish continuity in the interior of probability simplex meaningful upper lower bounds, e.g., we every entropy satisfying must lie bet...

Entropy games and matrix multiplication games have been recently introduced by Asarin et al. They model the situation in which one player (Despot) wishes to minimize the growth rate of a matrix product, whereas the other player (Tribune) wishes to maximize it. We develop an operator approach to entropy games. This allows us to show that entropy games can be cast as stochastic mean payoff games ...

We present a non-parametric method for calibrating jump-diffusion models to a finite set of observed option prices. We show that the usual formulations of the inverse problem via nonlinear least squares are illposed and propose a regularization method based on relative entropy: we reformulate our calibration problem into a problem of finding a risk neutral jump-diffusion model that reproduces t...

The aim of this work is to establish that two recently published projection theorems, one dealing with a parametric generalization of relative entropy and another dealing with Rényi divergence, are equivalent under a correspondence on the space of probability measures. Further, we demonstrate that the associated “Pythagorean” theorems are equivalent under this correspondence. Finally, we apply ...

Most preferred ordered weighted average (MP-OWA) operator is a new kind of neat (dynamic weight) OWA operator in the aggregation operator families. It considers the preferences of all alternatives across the criteria and provides unique aggregation characteristics in decision making. In this paper, we propose the parametric form of the MP-OWA operator to deal with the uncertainty preference inf...

In this paper the iterative methods of image restoration are considered. These methods are based on the successive approximation algorithm with adaptive regularization and parametric constrains on the solution. The adaptive regularization preserves the global image smoothing and is considered as the combined nonlinear operator for simultaneous removal of additive Gaussian and impulse noises. Th...