Rate of convergence of a particle method to the solution of the Mc Kean-Vlasov's equation

This paper studies the rate of convergence of an appropriatediscretization scheme of the solution of the Mc Kean-Vlasovequation introduced by Bossy and Talay. More specifically,we consider approximations of the distribution and of thedensity of the solution of the stochastic differentialequation associated to the Mc Kean - Vlasov equation. Thescheme adopted here is a mixed one: Euler/weakly interactingparticle system. If $n$ is the number of weakly interactingparticles and $h$ is the uniform step in the timediscretization, we prove that the rate of convergence of thedistribution functions of the approximating sequence in the $L^1(\Omega\times \Bbb R)$ norm and in the sup norm is of theorder of $\frac 1{\sqrt n} + h $, while for the densities is ofthe order $ h +\frac 1 {\sqrt {nh}}$. This result is obtainedby carefully employing techniques of Malliavin Calculus.

Inflation and output dynamics with firm-owned capital

We model firm-owned capital in a stochastic dynamic New-Keynesian generalequilibrium model à la Calvo. We find that this structure impliesequilibrium dynamics which are quantitatively di¤erent from the onesassociated with a benchmark case where households accumulate capital andrent it to firms. Our findings therefore stress the importance ofmodeling an investment decision at the firm level in addition to ameaningful price setting decision. Along the way we argue that the problemof modeling firm-owned capital with Calvo price-setting has not been solvedin a correct way in the previous literature.

Job dynamics, correlated shocks and wage profiles

We generalize the Mortensen-Pissarides (1994) model of the labor marketwith a more realistic structure for the stochastic process of theshocks to the worker-firm match. In this way we can acommodate theempirical observation that hazard rates of job termination decrease andaverage wages increase with job tenure. Besides being able to fit bettersome observables of the model, the changes we introduce are nontrivialfor the analysis of policies as well.

Cumulative frequency-dependent selective episodes allow for rapid morph cycles and rock-paper-scissors dynamics in species with overlapping generations.

Rock-paper-scissors (RPS) dynamics, which maintain genetic polymorphisms over time through negative frequency-dependent (FD) selection, can evolve in short-lived species with no generational overlap, where they produce rapid morph frequency cycles. However, most species have overlapping generations and thus, rapid RPS dynamics are thought to require stronger FD selection, the existence of which yet needs to be proved. Here, we experimentally demonstrate that two cumulative selective episodes, FD sexual selection reinforced by FD selection on offspring survival, generate sufficiently strong selection to generate rapid morph frequency cycles in the European common lizard Zootoca vivipara, a multi-annual species with major generational overlap. These findings show that the conditions required for the evolution of RPS games are fulfilled by almost all species exhibiting genetic polymorphisms and suggest that RPS games may be responsible for the maintenance of genetic diversity in a wide range of species.

Ispol'zovanie metodov teorii vosstanovleniia v modeliakh optimal'nogo dobyvaniia pishchi [Restoration theory in models of optimal feeding behavior]

The method of stochastic dynamic programming is widely used in ecology of behavior, but has some imperfections because of use of temporal limits. The authors presented an alternative approach based on the methods of the theory of restoration. Suggested method uses cumulative energy reserves per time unit as a criterium, that leads to stationary cycles in the area of states. This approach allows to study the optimal feeding by analytic methods.

Thermal activation and ATP dependence of the cytoskeleton remodeling dynamics

The cytoskeleton (CSK) is a nonequilibrium polymer network that uses hydrolyzable sources of free energy such as adenosine triphosphate (ATP) to remodel its internal structure. As in inert nonequilibrium soft materials, CSK remodeling has been associated with structural rearrangements driven by energy-activated processes. We carry out particle tracking and traction microscopy measurements of alveolar epithelial cells at various temperatures and ATP concentrations. We provide the first experimental evidence that the remodeling dynamics of the CSK is driven by structural rearrangements over free-energy barriers induced by thermally activated forces mediated by ATP. The measured activation energy of these forces is ~40kBTr (kB being the Boltzmann constant and Tr being the room temperature). Our experiments provide clues to understand the analogy between the dynamics of the living CSK and that of inert nonequilibrium soft materials.

Towards a theory of the credit-risk balance sheet (II). The evolution of its structure

This article has an immediate predecessor, upon which it is based and with which readers must necessarily be familiar: Towards a Theory of the Credit-Risk Balance Sheet (Vallverdú, Somoza and Moya, 2006). The Balance Sheet is conceptualised on the basis of the duality of a credit-based transaction; it deals with its theoretical foundations, providing evidence of a causal credit-risk duality, that is, a true causal relationship; its characteristics, properties and its static and dynamic characteristics are analyzed. This article, which provides a logical continuation to the previous one, studies the evolution of the structure of the Credit-Risk Balance Sheet as a consequence of a business¿s dynamics in the credit area. Given the Credit-Risk Balance Sheet of a company at any given time, it attempts to estimate, by means of sequential analysis, its structural evolution, showing its usefulness in the management and control of credit and risk. To do this, it bases itself, with the necessary adaptations, on the by-now classic works of Palomba and Cutolo. The establishment of the corresponding transformation matrices allows one to move from an initial balance sheet structure to a final, future one, to understand its credit-risk situation trends, as well as to make possible its monitoring and control, basic elements in providing support for risk management.

Towards a theory of the credit-risk balance sheet (II). The evolution of its structure

This article has an immediate predecessor, upon which it is based and with which readers must necessarily be familiar: Towards a Theory of the Credit-Risk Balance Sheet (Vallverdú, Somoza and Moya, 2006). The Balance Sheet is conceptualised on the basis of the duality of a credit-based transaction; it deals with its theoretical foundations, providing evidence of a causal credit-risk duality, that is, a true causal relationship; its characteristics, properties and its static and dynamic characteristics are analyzed. This article, which provides a logical continuation to the previous one, studies the evolution of the structure of the Credit-Risk Balance Sheet as a consequence of a business¿s dynamics in the credit area. Given the Credit-Risk Balance Sheet of a company at any given time, it attempts to estimate, by means of sequential analysis, its structural evolution, showing its usefulness in the management and control of credit and risk. To do this, it bases itself, with the necessary adaptations, on the by-now classic works of Palomba and Cutolo. The establishment of the corresponding transformation matrices allows one to move from an initial balance sheet structure to a final, future one, to understand its credit-risk situation trends, as well as to make possible its monitoring and control, basic elements in providing support for risk management.

The effect of plantation silviculture on soil organic matter and particle-size fractions in Amazonia

Eucalyptus grandis and other clonal plantations cover about 3.5 million ha in Brazil. The impacts of intensively-managed short-rotation forestry on soil aggregate structure and Carbon (C) dynamics are largely undocumented in tropical ecosystems. Long-term sustainability of these systems is probably in part linked to maintenance of soil organic matter and good soil structure and aggregation, especially in areas with low-fertility soils. This study investigated soil aggregate dynamics on a clay soil and a sandy soil, each with a Eucalyptus plantation and an adjacent primary forest. Silvicultural management did not reduce total C stocks, and did not change soil bulk density. Aggregates of the managed soils did not decrease in mass as hypothesized, which indicates that soil cultivation in 6 year cycles did not cause large decreases in soil aggregation in either soil texture. Silt, clay, and C of the sandy plantation soil shifted to greater aggregate protection, which may represent a decrease in C availability. The organic matter in the clay plantation soil increased in the fractions considered less protected while this shift from C to structural forms considered more protected was not observed.

Ruin Theory with Excess of Loss Reinsurance and Reinstatements

The present paper studies the probability of ruin of an insurer, if excess of loss reinsurance with reinstatements is applied. In the setting of the classical Cramer-Lundberg risk model, piecewise deterministic Markov processes are used to describe the free surplus process in this more general situation. It is shown that the finite-time ruin probability is both the solution of a partial integro-differential equation and the fixed point of a contractive integral operator. We exploit the latter representation to develop and implement a recursive algorithm for numerical approximation of the ruin probability that involves high-dimensional integration. Furthermore we study the behavior of the finite-time ruin probability under various levels of initial surplus and security loadings and compare the efficiency of the numerical algorithm with the computational alternative of stochastic simulation of the risk process. (C) 2011 Elsevier Inc. All rights reserved.

Diluted three-dimensional random field Ising model at zero temperature with metastable dynamics.

The influence of vacancy concentration on the behavior of the three-dimensional random field Ising model with metastable dynamics is studied. We have focused our analysis on the number of spanning avalanches which allows us a clear determination of the critical line where the hysteresis loops change from continuous to discontinuous. By a detailed finite-size scaling analysis we determine the phase diagram and numerically estimate the critical exponents along the whole critical line. Finally, we discuss the origin of the curvature of the critical line at high vacancy concentration.

Influence of the driving mechanism on the response of systems with athermal dynamics: The example of the random-field Ising model

We investigate the influence of the driving mechanism on the hysteretic response of systems with athermal dynamics. In the framework of local mean-field theory at finite temperature (but neglecting thermally activated processes), we compare the rate-independent hysteresis loops obtained in the random field Ising model when controlling either the external magnetic field H or the extensive magnetization M. Two distinct behaviors are observed, depending on disorder strength. At large disorder, the H-driven and M-driven protocols yield identical hysteresis loops in the thermodynamic limit. At low disorder, when the H-driven magnetization curve is discontinuous (due to the presence of a macroscopic avalanche), the M-driven loop is reentrant while the induced field exhibits strong intermittent fluctuations and is only weakly self-averaging. The relevance of these results to the experimental observations in ferromagnetic materials, shape memory alloys, and other disordered systems is discussed.