In this paper we introduce a notion of measure theoretical entropy for a finitely generated
free semigroup action and establish a variational principle when the semigroup is generated …

Given an onto map T acting on a metric space and an appropriate Banach space of
functions X (), one classically constructs for each potential A∈ X a transfer operator 多 A …

It is well known that in Information Theory and Machine Learning the Kullback-Leibler
divergence, which extends the concept of Shannon entropy, plays a fundamental role. Given …

Consider the shift acting on the Bernoulli space D f1; 2;:::; ng N. We denote OD f1; 2;:::; ng Z
D. We analyze several properties of the maximizing probability 1; A of a Hölder potential AW …

Statistical inference can be seen as information processing involving input information and
output information that updates belief about some unknown parameters. We consider the …

Abstract For, 0< λ< 1, consider the transformation T (x)= dx (mod 1) on the circle S^ 1, a C^ 1
function A: S^ 1 → R, and, the map F (x, s)=(T (x), λ\, s+ A (x)),(x, s) ∈ S^ 1 * R. We denote …

We study optimal transport for stationary stochastic processes taking values in finite spaces.
In order to reflect the stationarity of the underlying processes, we restrict attention to …

Given X, Y, Z and W, compact metric spaces, we consider two iterated function systems {τ x:
Z→ Z, x∈ X} and {τ y: W→ W, y∈ Y}, where τ x and τ y are contractions. Let Π (⋅,⋅, τ) be the …

Given two compact metric spaces $ X $ and $ Y $, a Lipschitz continuous cost function $ c $
on $ X\times Y $ and two probabilities $\mu\in\mathcal {P}(X),\,\nu\in\mathcal {P}(Y) $, we …

We introduce four, a priori different, concepts of topological pressure for possibly
discontinuous semiflows acting on a compact metric space and observe that they all agree …