Asymptotic Mean Stationarity of Sources With Finite Evolution Dimension

The notion of the emph{evolution} of a discrete random source with finite alphabet is introduced and its behavior under the action of an associated linear emph{evolution operator} is studied. Viewing these sources as possibly stable dynamical systems it is proved that all random sources with finite evolution dimension are asymptotically mean stationary, which implies that such random sources have ergodic properties and a well-defined entropy rate. It is shown that the class of random sources with finite evolution dimension properly generalizes the well-studied class of finitary stochastic processes, which includes (hidden) Markov sources as special cases

The ergodic decomposition of asymptotically mean stationary random sources

It is demonstrated how to represent asymptotically mean stationary (AMS) random sources with values in standard spaces as mixtures of ergodic AMS sources. This an extension of the well known decomposition of stationary sources which has facilitated the generalization of prominent source coding theorems to arbitrary, not necessarily ergodic, stationary sources. Asymptotic mean stationarity generalizes the definition of stationarity and covers a much larger variety of real-world examples of random sources of practical interest. It is sketched how to obtain source coding and related theorems for arbitrary, not necessarily ergodic, AMS sources, based on the presented ergodic decomposition.Comment: Submitted to IEEE Transactions on Information Theory, Apr. 200

Transverse coherence properties of X-ray beams in third-generation synchrotron radiation sources

This article describes a complete theory of spatial coherence for undulator radiation sources. Current estimations of coherence properties often assume that undulator sources are quasi-homogeneous, like thermal sources, and rely on the application of the van Cittert-Zernike theorem for calculating the degree of transverse coherence. Such assumption is not adequate when treating third generation light sources, because the vertical(geometrical) emittance of the electron beam is comparable or even much smaller than the radiation wavelength in a very wide spectral interval that spans over four orders of magnitude (from 0.1 Angstrom up to 10^3 Angstrom). Sometimes, the so-called Gaussian-Schell model, that is widely used in statistical optics in the description of partially-coherent sources, is applied as an alternative to the quasi-homogeneous model. However, as we will demonstrate, this model fails to properly describe coherent properties of X-ray beams from non-homogeneous undulator sources. As a result, a more rigorous analysis is required. We propose a technique, based on statistical optics and Fourier optics, to explicitly calculate the cross-spectral density of an undulator source in the most general case, at any position after the undulator. Our theory, that makes consistent use of dimensionless analysis, allows relatively easy treatment and physical understanding of many asymptotes of the parameter space, together with their region of applicability. Particular emphasis is given to the asymptotic situation when the horizontal emittance is much larger than the radiation wavelength, and the vertical emittance is arbitrary. This case is practically relevant for third generation synchrotron radiation sources.Comment: 71 pages, 20 figures - Version accepted for publication in Nuclear Inst. and Methods in Physics Research,

Characterization of ergodic hidden Markov sources

An algebraic criterim for the ergodicity of discrete random sources is presented. For finite-dimensional sources, which contain hidden Markov sources as a subclass, the criterium can be effectively computed. This result is obtained on the background of a novel, elementary theory of discrete random sources, which is based on linear spaces spanned by word functions, and linear operators on these spaces. An outline of basic elements of this theory is provided

Asymptotic mean stationarity and absolute continuity of point process distributions

This paper relates - for point processes $\Phi$ on $\mathbb{R}$ - two types of asymptotic mean stationarity (AMS) properties and several absolute continuity results for the common probability measures emerging from point process theory. It is proven that $\Phi$ is AMS under the time-shifts if and only if it is AMS under the event-shifts. The consequences for the accompanying two types of ergodic theorem are considered. Furthermore, the AMS properties are equivalent or closely related to several absolute continuity results. Thus, the class of AMS point processes is characterized in several ways. Many results from stationary point process theory are generalized for AMS point processes. To obtain these results, we first use Campbell's equation to rewrite the well-known Palm relationship for general nonstationary point processes into expressions which resemble results from stationary point process theory.Comment: Published in at http://dx.doi.org/10.3150/12-BEJ423 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm

Analyzing long-term correlated stochastic processes by means of recurrence networks: Potentials and pitfalls

Long-range correlated processes are ubiquitous, ranging from climate variables to financial time series. One paradigmatic example for such processes is fractional Brownian motion (fBm). In this work, we highlight the potentials and conceptual as well as practical limitations when applying the recently proposed recurrence network (RN) approach to fBm and related stochastic processes. In particular, we demonstrate that the results of a previous application of RN analysis to fBm (Liu \textit{et al.,} Phys. Rev. E \textbf{89}, 032814 (2014)) are mainly due to an inappropriate treatment disregarding the intrinsic non-stationarity of such processes. Complementarily, we analyze some RN properties of the closely related stationary fractional Gaussian noise (fGn) processes and find that the resulting network properties are well-defined and behave as one would expect from basic conceptual considerations. Our results demonstrate that RN analysis can indeed provide meaningful results for stationary stochastic processes, given a proper selection of its intrinsic methodological parameters, whereas it is prone to fail to uniquely retrieve RN properties for non-stationary stochastic processes like fBm.Comment: 8 pages, 6 figure

A re-examination of the Purchasing Power Parity using non-stationary dynamic panel methods : a comparative approach for developing and developed countries

The aim of this paper is to apply recent advances in the econometrics of non-stationary dynamic panel methods to examine the robustness of the PPP concept for a sample of 73 developed and developing countries. Our investigations indicate that the strong PPP is verified for OECD and MENA countries. However in Africa, Asia, Latin America and the PECO, PPP does not seem relevant to characterize the long-run behavior of the real exchange rate. A widening of our analysis field shows that the nature of the exchange rate regime doesn’t condition the validity of the PPP and that the PPP is more easily accepted in countries with high inflation than with low one.http://deepblue.lib.umich.edu/bitstream/2027.42/39956/3/wp570.pd

Numerical solution of gravitational dynamics in asymptotically anti-de Sitter spacetimes

A variety of gravitational dynamics problems in asymptotically anti-de Sitter (AdS) spacetime are amenable to efficient numerical solution using a common approach involving a null slicing of spacetime based on infalling geodesics, convenient exploitation of the residual diffeomorphism freedom, and use of spectral methods for discretizing and solving the resulting differential equations. Relevant issues and choices leading to this approach are discussed in detail. Three examples, motivated by applications to non-equilibrium dynamics in strongly coupled gauge theories, are discussed as instructive test cases. These are gravitational descriptions of homogeneous isotropization, collisions of planar shocks, and turbulent fluid flows in two spatial dimensions.Comment: 70 pages, 19 figures; v4: fixed minus sign typo in last term of eqn. (3.47

Health Care Expenditures in OECD Countries: A Panel Unit Root and Cointegration Analysis

This paper examines the linkationship between health care expenditures and gdp for 21 oecd countries using panel cointegration techniques. the analysis accounts for the fact that health care expenditures are not solely driven by income, but also by medical progress, where different measures are used. in the extended models, cointegration can be established. the income elasticity is not different from unity, implying that health care is not a luxury good. this finding is robust for alternative proxies of medical progress, and various estimators of the cointegration vector. in addition, cointegration can be detected even between nonstationary common factors.health care expenditures; medical progress, panel cointegration, common factors