Stochastic nonlinear Schrodinger equations driven by a fractional noise - Well posedness, large deviations and support

We consider stochastic nonlinear Schrodinger equations driven by an additive noise. The noise is fractional in time with Hurst parameter H in (0,1). It is also colored in space and the space correlation operator is assumed to be nuclear. We study the local well-posedness of the equation. Under adequate assumptions on the initial data, the space correlations of the noise and for some saturated nonlinearities, we prove a sample path large deviations principle and a support result. These results are stated in a space of exploding paths which are Holder continuous in time until blow-up. We treat the case of Kerr nonlinearities when H > 1/2

Bayesian Estimation of Inequalities with Non-Rectangular Censored Survey Data

Synthetic indices are used in Economics to measure various aspects of monetary inequalities. These scalar indices take as input the distribution over a finite population, for example the population of a specific country. In this article we consider the case of the French 2004 Wealth survey. We have at hand a partial measurement on the distribution of interest consisting of bracketed and sometimes missing data, over a subsample of the population of interest. We present in this article the statistical methodology used to obtain point and interval estimates taking into account the various uncertainties. The inequality indices being nonlinear in the input distribution, we rely on a simulation based approach where the model for the wealth per household is multivariate. Using the survey data as well as matched auxiliary tax declarations data, we have at hand a quite intricate non-rectangle multidimensional censoring. For practical issues we use a Bayesian approach. Inference using Monte-Carlo approximations relies on a Monte-Carlo Markov chain algorithm namely the Gibbs sampler. The quantities interesting to the decision maker are taken to be the various inequality indices for the French population. Their distribution conditional on the data of the subsample are assumed to be normal centered on the design-based estimates with variance computed through linearization and taking into account the sample design and total nonresponse. Exogeneous selection of the subsample, in particular the nonresponse mechanism, is assumed and we condition on the adequate covariates

N=1 SUSY AdS4 vacua in IIB SUGRA on group manifolds

We study N=1 compactification of IIB supergravity to AdS4. The internal manifold must have SU(2)-structure. By putting some restrictions on the SU(2) torsion classes, we can perform an exhaustive scan of all possible solutions on group manifolds. We show that sourceless solutions don't exist and that the presence of O5 and O7 orientifolds is mandatory. We also find a new solution and relate it by T-duality to a known type IIA solution with O6 planes.Comment: 22 pages, (v2) : Appendix on the name of the solvmanifold added, references updated, NS Bianchi Identity rewritte

Large deviations and support results for nonlinear Schrodinger equations with additive noise and applications

Sample path large deviations for the laws of the solutions of stochastic nonlinear Schrodinger equations when the noise converges to zero are presented. The noise is a complex additive gaussian noise. It is white in time and colored space wise. The solutions may be global or blow-up in finite time, the two cases are distinguished. The results are stated in trajectory spaces endowed with projective limit topologies. In this setting, the support of the law of the solution is also characterized. As a consequence, results on the law of the blow-up time and asymptotics when the noise converges to zero are obtained. An application to the transmission of solitary waves in fiber optics is also given

Exit from a basin of attraction for stochastic weakly damped nonlinear Schr\"odinger equations

We consider weakly damped nonlinear Schr\"odinger equations perturbed by a noise of small amplitude. The small noise is either complex and of additive type or real and of multiplicative type. It is white in time and colored in space. Zero is an asymptotically stable equilibrium point of the deterministic equations. We study the exit from a neighborhood of zero, invariant by the flow of the deterministic equation, in \xLtwo or in \xHone. Due to noise, large fluctuations off zero occur. Thus, on a sufficiently large time scale, exit from these domains of attraction occur. A formal characterization of the small noise asymptotic of both the first exit times and the exit points is given

Giant Planets

We review the interior structure and evolution of Jupiter, Saturn, Uranus and Neptune, and giant exoplanets with particular emphasis on constraining their global composition. Compared to the first edition of this review, we provide a new discussion of the atmospheric compositions of the solar system giant planets, we discuss the discovery of oscillations of Jupiter and Saturn, the significant improvements in our understanding of the behavior of material at high pressures and the consequences for interior and evolution models. We place the giant planets in our Solar System in context with the trends seen for exoplanets.Comment: This chapter is to be published in the second edition of the Treatise on Geophysics (Eds. T. Spohn, G. Schubert). 42 pages, 16 figures. Accepted 25 February 201

Common and Separate Ownership of Projects

This note points out the differences between conducting several projects within one big firm (common ownership) and conducting each project within an independent firm (separate ownership).Conglomerate, Nature of the firm, Market Vs hierarchies

Providing Long-term Care without Crowding-out Family Support and Private Insurance

In this paper we are interested in the organization of long-term care within a given population. Three care financers are identified: the family, the government and the care receiver who can buy a dependency insurance. Our interest lies in the effect of governmental intervention on the demand/supply of these three forms of LTC i.e. how state intervention affects the provision of LTC by the market and the family. Knowing that, we search for an efficient organization of LTC.