Ergodic properties of Poissonian ID processes

We show that a stationary IDp process (i.e., an infinitely divisible stationary process without Gaussian part) can be written as the independent sum of four stationary IDp processes, each of them belonging to a different class characterized by its L\'{e}vy measure. The ergodic properties of each class are, respectively, nonergodicity, weak mixing, mixing of all order and Bernoullicity. To obtain these results, we use the representation of an IDp process as an integral with respect to a Poisson measure, which, more generally, has led us to study basic ergodic properties of these objects.Comment: Published at http://dx.doi.org/10.1214/009117906000000692 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org

Poisson-Pinsker factor and infinite measure preserving group actions

We solve the question of the existence of a Poisson-Pinsker factor for conservative ergodic infinite measure preserving action of a countable amenable group by proving the following dichotomy: either it has totally positive Poisson entropy (and is of zero type), or it possesses a Poisson-Pinsker factor. If G is abelian and the entropy positive, the spectrum is absolutely continuous (Lebesgue countable if G=\mathbb{Z}) on the whole L^{2}-space in the first case and in the orthocomplement of the L^{2}-space of the Poisson-Pinsker factor in the second.Comment: 9 page

Maharam extension and stationary stable processes

We give a second look at stationary stable processes by interpreting the self-similar property at the level of the L\'evy measure as characteristic of a Maharam system. This allows us to derive structural results and their ergodic consequences.Comment: Published in at http://dx.doi.org/10.1214/11-AOP671 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org

Cost reducing investiment, competition and industry dynamics

We characterize the dynamic equilibrium path ofa competitive industry with free entry and exit, where atomistic fmns undertake investment over time in order to reduce their future production costs. Investment reduces both total as well as marginal cost of production; however, the associated dynamic scale economies are eventually bounded. Cost reduction is deterministic and there are no inter-firm spill-overs. Marginal cost in any time period is stricdy increasing in output and active firms incur a positive fixed cost even if no output is produced. The industry equilibrium path is socially optimal. Equilibrium prices are (weakly) decreasing over time. Firms invest in cost reduction and eam negative net profit when they are young. In later periods, they face prices aboye their mínimum average cost, produce beyond their mínimum efficient scale and eam strictly positive net profit. No frrm enters after the initial time periodo Though all fmns are ex ante identical, sorne fmns may exit before others (shake-out). Exiting fmns have relatively "small size" compared to incumbents; as the industry matures, concentration and the average size of incumbent fmns increase. Heterogeneity in behaviour and size of fmns emerges endogenously through differences in their length of stay in the industry

Sources of Welfare Disparities across and within Regions of Brazil: Evidence from the 2002-03 Household Budget Survey

Brazil's inequalities in welfare and poverty across and within regions can be accounted for by differences in household attributes and returns to those attributes. This paper uses Oaxaca-Blinder decompositions at the mean as well as at different quantiles of welfare distributions on regionally representative household survey data (2002-03 Household Budget Survey). The analysis finds that household attributes account for most of the welfare differences between urban and rural areas within regions. However, comparing the lagging Northeast region with the leading Southeast region, differences in returns to attributes account for a large part of the welfare disparities, in particular in metropolitan areas, supporting the presence of agglomeration effects in booming areas.Brazil; Leading and Lagging Regions; Welfare; Poverty; Oaxaca-Blinder decompositions

Cost reducing investiment, competition and industry dynamics.

We characterize the dynamic equilibrium path ofa competitive industry with free entry and exit, where atomistic fmns undertake investment over time in order to reduce their future production costs. Investment reduces both total as well as marginal cost of production; however, the associated dynamic scale economies are eventually bounded. Cost reduction is deterministic and there are no inter-firm spill-overs. Marginal cost in any time period is stricdy increasing in output and active firms incur a positive fixed cost even if no output is produced. The industry equilibrium path is socially optimal. Equilibrium prices are (weakly) decreasing over time. Firms invest in cost reduction and eam negative net profit when they are young. In later periods, they face prices aboye their mínimum average cost, produce beyond their mínimum efficient scale and eam strictly positive net profit. No frrm enters after the initial time periodo Though all fmns are ex ante identical, sorne fmns may exit before others (shake-out). Exiting fmns have relatively "small size" compared to incumbents; as the industry matures, concentration and the average size of incumbent fmns increase. Heterogeneity in behaviour and size of fmns emerges endogenously through differences in their length of stay in the industry.Cost Reduction; Investment; Learning; Dynamic Competitive Equilibrium; Shake Out;

Joining primeness and disjointness from infinitely divisible systems

We show that ergodic dynamical systems generated by infinitely divisible stationary processes are disjoint in the sense of Furstenberg with distally simple systems and systems whose maximal spectral type is singular with respect to the convolution of any two continuous measures.Comment: 15 page

Poisson suspensions and infinite ergodic theory

We investigate ergodic theory of Poisson suspensions. In the process, we establish close connections between finite and infinite measure preserving ergodic theory. Poisson suspensions thus provide a new approach to infinite measure preserving ergodic theory. Fields investigated here are mixing properties, spectral theory, joinings. We also compare Poisson suspensions to the apparently similar looking Gaussian dynamical systems.Comment: 18 page

The learning curve in a competitive industry.

We consider the learning curve in an industry with free entry and exit, and price-taking firms. A unique equilibrium exists if the fixed cost is positive. While equilibrium profits are zero, mature firms earn rents on their learning, and, if costs are convex, no firm can profitably enter after the date the industry begins. Under some cost and demand conditions, however, firms may have to exit the market despite their experience gained earlier. Furthermore identical firms facing the same prices may produce different quantities. The market outcome is always socially efficient, even if dictates that firms exit after learning. Finally, actual and optimal industry concentration does not always increase in the intensity of learning.Learning curve; Industry evolution; Perfect competition;

Invariant measures for Cartesian powers of Chacon infinite transformation

We describe all boundedly finite measures which are invariant by Cartesian powers of an infinite measure preserving version of Chacon transformation. All such ergodic measures are products of so-called diagonal measures, which are measures generalizing in some way the measures supported on a graph. Unlike what happens in the finite-measure case, this class of diagonal measures is not reduced to measures supported on a graph arising from powers of the transformation: it also contains some weird invariant measures, whose marginals are singular with respect to the measure invariant by the transformation. We derive from these results that the infinite Chacon transformation has trivial centralizer, and has no nontrivial factor. At the end of the paper, we prove a result of independent interest, providing sufficient conditions for an infinite measure preserving dynamical system defined on a Cartesian product to decompose into a direct product of two dynamical systems