Intensity correlation functions of dye lasers: Comparison of colored-gain-noise and colored-loss-noise models

The intensity correlation functions C(t) for the colored-gain-noise model of dye lasers are analyzed and compared with those for the loss-noise model. For correlation times ¿ larger than the deterministic relaxation time td, we show with the use of the adiabatic approximation that C(t) values coincide for both models. For small correlation times we use a method that provides explicit expressions of non-Markovian correlation functions, approximating simultaneously short- and long-time behaviors. Comparison with numerical simulations shows excellent results simultaneously for short- and long-time regimes. It is found that, when the correlation time of the noise increases, differences between the gain- and loss-noise models tend to disappear. The decay of C(t) for both models can be described by a time scale that approaches the deterministic relaxation time. However, in contrast with the loss-noise model, a secondary time scale remains for large times for the gain-noise model, which could allow one to distinguish between both models.

Image restoration in astronomy: a Bayesian perspective

When preparing an article on image restoration in astronomy, it is obvious that some topics have to be dropped to keep the work at reasonable length. We have decided to concentrate on image and noise models and on the algorithms to find the restoration. Topics like parameter estimation and stopping rules are also commented on. We start by describing the Bayesian paradigm and then proceed to study the noise and blur models used by the astronomical community. Then the prior models used to restore astronomical images are examined. We describe the algorithms used to find the restoration for the most common combinations of degradation and image models. Then we comment on important issues such as acceleration of algorithms, stopping rules, and parameter estimation. We also comment on the huge amount of information available to, and made available by, the astronomical community.

Well-posedness and invariant measures for HJM models with deterministic volatility and Lévy noise

We give sufficient conditions for existence, uniqueness and ergodicity of invariant measures for Musiela's stochastic partial differential equation with deterministic volatility and a Hilbert space valued driving Lévy noise. Conditions for the absence of arbitrage and for the existence of mild solutions are also discussed.

Analysis of nonlinear noisy integrate & fire neuron models: blow-up and steady states

Nonlinear Noisy Leaky Integrate and Fire (NNLIF) models for neurons networks can be written as Fokker-Planck-Kolmogorov equations on the probability density of neurons, the main parameters in the model being the connectivity of the network and the noise. We analyse several aspects of the NNLIF model: the number of steady states, a priori estimates, blow-up issues and convergence toward equilibrium in the linear case. In particular, for excitatory networks, blow-up always occurs for initial data concentrated close to the firing potential. These results show how critical is the balance between noise and excitatory/inhibitory interactions to the connectivity parameter.

Noise-induced scenario for inverted phase diagrams

We introduce a class of exactly solvable models exhibiting an ordering noise-induced phase transition in which order arises as a result of a balance between the relaxing deterministic dynamics and the randomizing character of the fluctuations. A finite-size scaling analysis of the phase transition reveals that it belongs to the universality class of the equilibrium Ising model. All these results are analyzed in the light of the nonequilibrium probability distribution of the system, which can be obtained analytically. Our results could constitute a possible scenario of inverted phase diagrams in the so-called lower critical solution temperature transitions.

Stochastic processes induced by dichotomous markov noise: Some exact dynamical results

Stochastic processes defined by a general Langevin equation of motion where the noise is the non-Gaussian dichotomous Markov noise are studied. A non-FokkerPlanck master differential equation is deduced for the probability density of these processes. Two different models are exactly solved. In the second one, a nonequilibrium bimodal distribution induced by the noise is observed for a critical value of its correlation time. Critical slowing down does not appear in this point but in another one.

Noise and dynamics of self-organized critical phenomena

Different microscopic models exhibiting self-organized criticality are studied numerically and analytically. Numerical simulations are performed to compute critical exponents, mainly the dynamical exponent, and to check universality classes. We find that various models lead to the same exponent, but this universality class is sensitive to disorder. From the dynamic microscopic rules we obtain continuum equations with different sources of noise, which we call internal and external. Different correlations of the noise give rise to different critical behavior. A model for external noise is proposed that makes the upper critical dimensionality equal to 4 and leads to the possible existence of a phase transition above d=4. Limitations of the approach of these models by a simple nonlinear equation are discussed.

Power supply noise and logic error probability

Voltage fluctuations caused by parasitic impedances in the power supply rails of modern ICs are a major concern in nowadays ICs. The voltage fluctuations are spread out to the diverse nodes of the internal sections causing two effects: a degradation of performances mainly impacting gate delays anda noisy contamination of the quiescent levels of the logic that drives the node. Both effects are presented together, in thispaper, showing than both are a cause of errors in modern and future digital circuits. The paper groups both error mechanismsand shows how the global error rate is related with the voltage deviation and the period of the clock of the digital system.

Local noise analysis of a Schottky contact: combined thermionic-emissiondiffusion theory

A theoretical model for the noise properties of Schottky barrier diodes in the framework of the thermionic-emission¿diffusion theory is presented. The theory incorporates both the noise inducedby the diffusion of carriers through the semiconductor and the noise induced by the thermionicemission of carriers across the metal¿semiconductor interface. Closed analytical formulas arederived for the junction resistance, series resistance, and contributions to the net noise localized indifferent space regions of the diode, all valid in the whole range of applied biases. An additionalcontribution to the voltage-noise spectral density is identified, whose origin may be traced back tothe cross correlation between the voltage-noise sources associated with the junction resistance andthose for the series resistance. It is argued that an inclusion of the cross-correlation term as a newelement in the existing equivalent circuit models of Schottky diodes could explain the discrepanciesbetween these models and experimental measurements or Monte Carlo simulations.

Local noise analysis of a Schottky contact: combined thermionic-emissiondiffusion theory

A theoretical model for the noise properties of Schottky barrier diodes in the framework of the thermionic-emission¿diffusion theory is presented. The theory incorporates both the noise inducedby the diffusion of carriers through the semiconductor and the noise induced by the thermionicemission of carriers across the metal¿semiconductor interface. Closed analytical formulas arederived for the junction resistance, series resistance, and contributions to the net noise localized indifferent space regions of the diode, all valid in the whole range of applied biases. An additionalcontribution to the voltage-noise spectral density is identified, whose origin may be traced back tothe cross correlation between the voltage-noise sources associated with the junction resistance andthose for the series resistance. It is argued that an inclusion of the cross-correlation term as a newelement in the existing equivalent circuit models of Schottky diodes could explain the discrepanciesbetween these models and experimental measurements or Monte Carlo simulations.

A Rembrandt is a Rembrandt

As paintings are assets, we propose to model a painting's price dynamics as a diffusion process, i.e., as the financial literature models share prices, but correcting by size. We show that the influence of size on the artwork price diminishes as the paintings gets older because 1) prices incorporate progressively more noise and 2) for high quality artists, the relative importance of size on price decreases as the artist consolidates and authorship gains importance as explanatory variable. Our theoretical results are consistent with data from a sample of 19th- and 20th-century Catalan painters of similar quality. These findings suggest that an artist's quality and antiquity should be taken into account in order to obtain more efficient estimates of parameters in hedonic art market models.

Parametric and semiparametric estimation of sample selection models: an empirical application to the female labour force in Portugal

This comment corrects the errors in the estimation process that appear in Martins (2001). The first error is in the parametric probit estimation, as the previously presented results do not maximize the log-likelihood function. In the global maximum more variables become significant. As for the semiparametric estimation method, the kernel function used in Martins (2001) can take on both positive and negative values, which implies that the participation probability estimates may be outside the interval [0,1]. We have solved the problem by applying local smoothing in the kernel estimation, as suggested by Klein and Spady (1993).

Are one factor logarithmic volatility models useful to fit the features of financial data? An application to microsoft data.

This paper provides empirical evidence that continuous time models with one factor of volatility, in some conditions, are able to fit the main characteristics of financial data. It also reports the importance of the feedback factor in capturing the strong volatility clustering of data, caused by a possible change in the pattern of volatility in the last part of the sample. We use the Efficient Method of Moments (EMM) by Gallant and Tauchen (1996) to estimate logarithmic models with one and two stochastic volatility factors (with and without feedback) and to select among them.

Subjective income expectations, canonical models and income risk

Expectations are central to behaviour. Despite the existence of subjective expectations data, the standard approach is to ignore these, to hypothecate a model of behaviour and to infer expectations from realisations. In the context of income models, we reveal the informational gain obtained from using both a canonical model and subjective expectations data. We propose a test for this informational gain, and illustrate our approach with an application to the problem of measuring income risk.