Turn-on-time statistics of modulated lasers subjected to resonant weak optical feedback

We present analytical calculations of the turn-on-time probability distribution of intensity-modulated lasers under resonant weak optical feedback. Under resonant conditions, the external cavity round-trip time is taken to be equal to the modulation period. The probability distribution of the solitary laser results are modified to give reduced values of the mean turn-on-time and its variance. Numerical simulations have been carried out showing good agreement with the analytical results.

First-passage-time statistics for diffusion processes with an external random force

We present exact equations and expressions for the first-passage-time statistics of dynamical systems that are a combination of a diffusion process and a random external force modeled as dichotomous Markov noise. We prove that the mean first passage time for this system does not show any resonantlike behavior.

Dynamics of sweeping through an instability: Passage-time statistics for colored noise

A calculation of passage-time statistics is reported for the laser switch-on problem, under the influence of colored noise, when the net gain is continuously swept from below to above threshold. Cases of fast and slow sweeping are considered. In the weak-noise limit, asymptotic results are given for small and large correlation times of the noise. The mean first passage time increases with the correlation time of the noise. This effect is more important for fast sweeping than for slow sweeping.

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First-passage times for non-Markovian processes

First-passage time statistics for non-Markovian processes have heretofore only been developed for processes driven by dichotomous fluctuations that are themselves Markov. Herein we develop a new method applicable to Markov and non-Markovian dichotomous fluctuations and calculate analytic mean first-passage times for particular examples.

First-passage times for non-Markovian processes: Correlated impacts on a free process

We develop a method to obtain first-passage-time statistics for non-Markovian processes driven by dichotomous fluctuations. The fluctuations themselves need not be Markovian. We calculate analytic first-passage-time distributions and mean first-passage times for exponential, rectangular, and long-tail temporal distributions of the fluctuations.

First-passage times for non-Markovian processes: Correlated impacts on bound processes

Our previously developed stochastic trajectory analysis technique has been applied to the calculation of first-passage time statistics of bound processes. Explicit results are obtained for linearly bound processes driven by dichotomous fluctuations having exponential and rectangular temporal distributions.

First-passage times for non-Markovian processes: Shot noise

The stochastic-trajectory-analysis technique is applied to the calculation of the mean¿first-passage-time statistics for processes driven by external shot noise. Explicit analytical expressions are obtained for free and bound processes.

Reliable detection of directional couplings using rank statistics

To detect directional couplings from time series various measures based on distances in reconstructed state spaces were introduced. These measures can, however, be biased by asymmetries in the dynamics' structure, noise color, or noise level, which are ubiquitous in experimental signals. Using theoretical reasoning and results from model systems we identify the various sources of bias and show that most of them can be eliminated by an appropriate normalization. We furthermore diminish the remaining biases by introducing a measure based on ranks of distances. This rank-based measure outperforms existing distance-based measures concerning both sensitivity and specificity for directional couplings. Therefore, our findings are relevant for a reliable detection of directional couplings from experimental signals.

Strategies for sequential prediction of stationary time series

We present simple procedures for the prediction of a real valued sequence. The algorithms are based on a combinationof several simple predictors. We show that if the sequence is a realization of a bounded stationary and ergodic random process then the average of squared errors converges, almost surely, to that of the optimum, given by the Bayes predictor. We offer an analog result for the prediction of stationary gaussian processes.

Improved nonparametric confidence intervals in time series regressions

Condence intervals in econometric time series regressions suffer fromnotorious coverage problems. This is especially true when the dependencein the data is noticeable and sample sizes are small to moderate, as isoften the case in empirical studies. This paper suggests using thestudentized block bootstrap and discusses practical issues, such as thechoice of the block size. A particular data-dependent method is proposedto automate the method. As a side note, it is pointed out that symmetricconfidence intervals are preferred over equal-tailed ones, since theyexhibit improved coverage accuracy. The improvements in small sampleperformance are supported by a simulation study.

The impact of "early" nineteenth-century globalization on foreign trade in the Southern Cone: A study of British trade statistics

This paper deals with the impact of "early" nineteenth-century globalization (c.1815-1860) on foreign trade in the Southern Cone (SC). Most of the evidence is drawn from bilateral trades between Britain and the SC, at a time when Britain was the main commercial partner of the new republics. The main conclusion drawn is that early globalization had a positive impact on foreign trade in the SC, and this was due to: improvements in the SC's terms of trade during this period; the SC's per capita consumption of textiles (the main manufacture traded on world markets at that time) increased substantially during this period, at a time when clothing was one of the main items of SC household budgets; British merchants brought with them capital, shipping, insurance, and also facilitated the formation of vast global networks, which further promoted the SC's exports to a wider range of outlets.

On the closed-form approximation of short-time random strike options

In this paper we propose a general technique to develop first and second order closed-form approximation formulas for short-time options withrandom strikes. Our method is based on Malliavin calculus techniques andallows us to obtain simple closed-form approximation formulas dependingon the derivative operator. The numerical analysis shows that these formulas are extremely accurate and improve some previous approaches ontwo-assets and three-assets spread options as Kirk's formula or the decomposition mehod presented in Alòs, Eydeland and Laurence (2011).

Probabilistic maximal covering location-allocation models with constrained waiting time or queue length for congested systems

When dealing with the design of service networks, such as healthand EMS services, banking or distributed ticket selling services, thelocation of service centers has a strong influence on the congestion ateach of them, and consequently, on the quality of service. In this paper,several models are presented to consider service congestion. The firstmodel addresses the issue of the location of the least number of single--servercenters such that all the population is served within a standard distance,and nobody stands in line for a time longer than a given time--limit, or withmore than a predetermined number of other clients. We then formulateseveral maximal coverage models, with one or more servers per service center.A new heuristic is developed to solve the models and tested in a 30--nodesnetwork.

A Hull and White formula for a general stochastic volatility jump-diffusion model with applications to the study of the short-time behavior of the implied volatility

In this paper, generalizing results in Alòs, León and Vives (2007b), we see that the dependence of jumps in the volatility under a jump-diffusion stochastic volatility model, has no effect on the short-time behaviour of the at-the-money implied volatility skew, although the corresponding Hull and White formula depends on the jumps. Towards this end, we use Malliavin calculus techniques for Lévy processes based on Løkka (2004), Petrou (2006), and Solé, Utzet and Vives (2007).