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Exploiting the geometric nature of statistical divergences, we devise a way to define associated induced uncertainty measures for discrete and finite probability distributions. We also report new uncertainty measures and discuss their…
We consider endomorphisms of a compact manifold which are expanding except for a finite number of points and prove the existence and uniqueness of a physical measure and its stochastical stability. We also characterize the zero-noise limit…
We show that any ergodic measure for a piecewise monotonic map with positive metric entropy is approximated by periodic measures in the weak-* sense. This partially answers Hofbauer-Raith's conjecture.
We sharpen an estimate for the growth rate of preimages of a point under a transitive piecewise monotone interval map. Then we apply our estimate to study the continuity of the operator which assigns to such a map its constant slope model.
Piecewise Deterministic Markov Processes (PDMPs) are studied in a general framework. First, different constructions are proven to be equivalent. Second, we introduce a coupling between two PDMPs following the same differential flow which…
We study a random dynamical system such that one transformation is randomly selected from a family of transformations and then applied on each iteration. For such random dynamical systems, we consider estimates of absolutely continuous…
The regularity of monotone transport maps plays an important role in several applications to PDE and geometry. Unfortunately, the classical statements on this subject are restricted to the case when the measures are compactly supported. In…
We address the common problem of calculating intervals in the presence of systematic uncertainties. We aim to investigate several approaches, but here describe just a Bayesian technique for setting upper limits. The particular example we…
The aim of this article is to establish basic results in a conditional measure theory. The results are applied to prove that arbitrary kernels and conditional distributions are represented by measures in a conditional set theory. In…
We define the empiric stochastic stability of an invariant measure in the finite-time scenario, the classical definition of stochastic stability. We prove that an invariant measure of a continuous system is empirically stochastically stable…
We study the statistical properties of piecewise expanding maps in the general setting of metric measure spaces. We provide sufficient conditions for exponential mixing of such systems with explicit estimates on the constants. We also…
We consider the equilibrium problem for an external background potential in weighted potential theory, and show that for a large class of background potentials there is a complementarity relationship between the measure solving the weighted…
A general theory is provided delivering convergence of maximal cyclically monotone mappings containing the supports of coupling measures of sequences of pairs of possibly random probability measures on Euclidean space. The theory is based…
This paper studies the problem of testing whether a function is monotone from a nonparametric Bayesian perspective. Two new families of tests are constructed. The first uses constrained smoothing splines, together with a hierarchical…
The aim of this paper is to show how extracting dynamical behavior and ergodic properties from deterministic chaos with the assistance of exact invariant measures. On the one hand, we provide an approach to deal with the inverse problem of…
We focus on the problem estimating a monotone trend function under additive and dependent noise. New point-wise confidence interval estimators under both short- and long-range dependent errors are introduced and studied. These intervals are…
We examine a family of intrinsic performance measures in terms of probability distributions that generalize Hellinger distance and Fisher information. They are applied to quantum metrology to assess the uncertainty in the detection of…
This paper reports on the application to field measurements of time series methods developed on the basis of the theory of deterministic chaos. The major difficulties are pointed out that arise when the data cannot be assumed to be purely…
The unitary transformation of path-integral differential measure is described. The main properties of perturbation theory in the phase space of action-angle, energy-time variables are investigated. The measure in cylindrical coordinates is…
A class of piecewise affine hyperbolic maps on a bounded subset of the plane is considered. It is shown that if a map from this class is sufficiently area-expanding then almost surely this map has an absolutely continuous invariant measure.