Boltzmann equation for dissipative gases in homogeneous states with nonlinear friction

Combining analytical and numerical methods, we study within the framework of the homogeneous non-linear Boltzmann equation, a broad class of models relevant for the dynamics of dissipative fluids, including granular gases. We use the new method presented in a previous paper [J. Stat. Phys. 124, 549 (2006)] and extend our results to a different heating mechanism, namely a deterministic non-linear friction force. We derive analytically the high energy tail of the velocity distribution and compare the theoretical predictions with high precision numerical simulations. Stretched exponential forms are obtained when the non-equilibrium steady state is stable. We derive sub-leading corrections and emphasize their relevance. In marginal stability cases, power-law behaviors arise, with exponents obtained as the roots of transcendental equations. We also consider some simple BGK (Bhatnagar, Gross, Krook) models, driven by similar heating devices, to test the robustness of our predictions

La stationnarité en économétrie et en macroéconomique : un guide pour les non initiés

Le but de ce texte est de présenter une introduction non technique à l’utilisation et à l’importance de séries chronologiques non stationnaires en économétrie et en macroéconomique. Les sujets suivants font l’objet de la présentation : la distinction entre tendances stochastiques et tendances déterministes; les tests d’hypothèse pour discriminer entre séries non stationnaires avec tendances stochastiques, d’une part, et, d’autre part, séries qui sont stationnaires autour de tendances déterministes; les conséquences de la non-stationnarité pour la théorie macroéconomique; les tests de stationnarité en présence de changements structurels; l’estimation de modèles économétriques avec variables qui sont individuellement non stationnaires.The paper gives a non-technical introduction to non-stationary time series and considers their importance in macro-econometrics and macroeconomics. The following topics are discussed: the distinction between stochastic and deterministic trends; statistical tests for discriminating between non-stationary series with stochastic trends and series which are stationary or which are stationnary around a deterministic time trend; the importance of unit roots for macroeconomic theory; structural breaks and tests for stochastic trends; the estimation of time series models with non-stationary variables; the existence of stable relationships among variables which are individually non-stationary

An Empirical Analysis of the Credit-Output Relationship: Evidence from Peru

This paper investigates the empirical relationship between credit and output in Peru. The analysis is based on the estimation of vector error correction models and the identification of structural shocks. The models considered include real output, real credit growth (in domestic currency, foreign currency and both), and terms of trade. Using quarterly data for the period 1994-2011, the results suggest that real credit growth contain useful information to understand the evolution of the non-deterministic component of real output. In particular, the results show that: (i) there exist a stable long-run relationship between real credit growth, output and terms of trade, (ii) real credit growth is useful in forecasting output in the long-run, and (iii) a structural permanent shock in real credit has positive permanent effects on output. Therefore, credit aggregates could be useful as indicator variables for policymakers.Credit growth, output growth, vector error correction models, structural shocks.

Learning and equilibrium selection in a monetary overlapping generations model with sticky prices

We study adaptive learning in a monetary overlapping generations model with sticky prices and monopolistic competition for the case where learning agents observe current endogenous variables. Observability of current variables is essential for informational consistency of the learning setup with the model set up but generates multiple temporary equilibria when prices are flexible and prevents a straightforward construction of the learning dynamics. Sticky prices overcome this problem by avoiding simultaneity between prices and price expectations. Adaptive learning then robustly selects the determinate (monetary) steady state independent from the degree of imperfect competition. The indeterminate (non-monetary) steady state and non-stationary equilibria are never stable. Stability in a deterministic version of the model may differ because perfect foresight equilibria can be the limit of restricted perceptions equilibria of the stochastic economy with vanishing noise and thereby inherit different stability properties. This discontinuity at the zero variance of shocks suggests to analyze learning in stochastic models

La stationnarité en économétrie et en macroéconomique : un guide pour les non initiés

The paper gives a non-technical introduction to non-stationary time series and considers their importance in macro-econometrics and macroeconomics. The following topics are discussed: the distinction between stochastic and deterministic trends; statistical tests for discriminating between non-stationary series with stochastic trends and series which are stationary or which are stationnary around a deterministic time trend; the importance of unit roots for macroeconomic theory; structural breaks and tests for stochastic trends; the estimation of time series models with non-stationary variables; the existence of stable relationships among variables which are individually non-stationary. Le but de ce texte est de présenter une introduction non technique à l’utilisation et à l’importance de séries chronologiques non stationnaires en économétrie et en macroéconomique. Les sujets suivants font l’objet de la présentation : la distinction entre tendances stochastiques et tendances déterministes; les tests d’hypothèse pour discriminer entre séries non stationnaires avec tendances stochastiques, d’une part, et, d’autre part, séries qui sont stationnaires autour de tendances déterministes; les conséquences de la non-stationnarité pour la théorie macroéconomique; les tests de stationnarité en présence de changements structurels; l’estimation de modèles économétriques avec variables qui sont individuellement non stationnaires.

A general class of spreading processes with non-Markovian dynamics

In this paper we propose a general class of models for spreading processes we call the $SI^*V^*$ model. Unlike many works that consider a fixed number of compartmental states, we allow an arbitrary number of states on arbitrary graphs with heterogeneous parameters for all nodes and edges. As a result, this generalizes an extremely large number of models studied in the literature including the MSEIV, MSEIR, MSEIS, SEIV, SEIR, SEIS, SIV, SIRS, SIR, and SIS models. Furthermore, we show how the $SI^*V^*$ model allows us to model non-Poisson spreading processes letting us capture much more complicated dynamics than existing works such as information spreading through social networks or the delayed incubation period of a disease like Ebola. This is in contrast to the overwhelming majority of works in the literature that only consider spreading processes that can be captured by a Markov process. After developing the stochastic model, we analyze its deterministic mean-field approximation and provide conditions for when the disease-free equilibrium is stable. Simulations illustrate our results

Intensional and Extensional Semantics of Bounded and Unbounded Nondeterminism

We give extensional and intensional characterizations of nondeterministic functional programs: as structure preserving functions between biorders, and as nondeterministic sequential algorithms on ordered concrete data structures which compute them. A fundamental result establishes that the extensional and intensional representations of non-deterministic programs are equivalent, by showing how to construct a unique sequential algorithm which computes a given monotone and stable function, and describing the conditions on sequential algorithms which correspond to continuity with respect to each order. We illustrate by defining may and must-testing denotational semantics for a sequential functional language with bounded and unbounded choice operators. We prove that these are computationally adequate, despite the non-continuity of the must-testing semantics of unbounded nondeterminism. In the bounded case, we prove that our continuous models are fully abstract with respect to may and must-testing by identifying a simple universal type, which may also form the basis for models of the untyped lambda-calculus. In the unbounded case we observe that our model contains computable functions which are not denoted by terms, by identifying a further "weak continuity" property of the definable elements, and use this to establish that it is not fully abstract