First-passage-time noninteger moments for some diffusion and dichotomous processes

We calculate noninteger moments ¿tq¿ of first passage time to trapping, at both ends of an interval (0,L), for some diffusion and dichotomous processes. We find the critical behavior of ¿tq¿, as a function of q, for free processes. We also show that the addition of a potential can destroy criticality.

Fractal dimension for Gaussian colored processes

The exact analytical expression for the Hausdorff dimension of free processes driven by Gaussian noise in n-dimensional space is obtained. The fractal dimension solely depends on the time behavior of the arbitrary correlation function of the noise, ranging from DX=1 for Orstein-Uhlenbeck input noise to any real number greater than 1 for fractional Brownian motions.

A post-processing pipeline to reconstruct the developing fetal brain using low-resolution MRI

Introduction. Development of the fetal brain surfacewith concomitant gyrification is one of the majormaturational processes of the human brain. Firstdelineated by postmortem studies or by ultrasound, MRIhas recently become a powerful tool for studying in vivothe structural correlates of brain maturation. However,the quantitative measurement of fetal brain developmentis a major challenge because of the movement of the fetusinside the amniotic cavity, the poor spatial resolution,the partial volume effect and the changing appearance ofthe developing brain. Today extensive efforts are made todeal with the âeurooepost-acquisitionâeuro reconstruction ofhigh-resolution 3D fetal volumes based on severalacquisitions with lower resolution (Rousseau, F., 2006;Jiang, S., 2007). We here propose a framework devoted tothe segmentation of the basal ganglia, the gray-whitetissue segmentation, and in turn the 3D corticalreconstruction of the fetal brain. Method. Prenatal MRimaging was performed with a 1-T system (GE MedicalSystems, Milwaukee) using single shot fast spin echo(ssFSE) sequences in fetuses aged from 29 to 32gestational weeks (slice thickness 5.4mm, in planespatial resolution 1.09mm). For each fetus, 6 axialvolumes shifted by 1 mm were acquired (about 1 min pervolume). First, each volume is manually segmented toextract fetal brain from surrounding fetal and maternaltissues. Inhomogeneity intensity correction and linearintensity normalization are then performed. A highspatial resolution image of isotropic voxel size of 1.09mm is created for each fetus as previously published byothers (Rousseau, F., 2006). B-splines are used for thescattered data interpolation (Lee, 1997). Then, basalganglia segmentation is performed on this superreconstructed volume using active contour framework witha Level Set implementation (Bach Cuadra, M., 2010). Oncebasal ganglia are removed from the image, brain tissuesegmentation is performed (Bach Cuadra, M., 2009). Theresulting white matter image is then binarized andfurther given as an input in the Freesurfer software(http://surfer.nmr.mgh.harvard.edu/) to provide accuratethree-dimensional reconstructions of the fetal brain.Results. High-resolution images of the cerebral fetalbrain, as obtained from the low-resolution acquired MRI,are presented for 4 subjects of age ranging from 29 to 32GA. An example is depicted in Figure 1. Accuracy in theautomated basal ganglia segmentation is compared withmanual segmentation using measurement of Dice similarity(DSI), with values above 0.7 considering to be a verygood agreement. In our sample we observed DSI valuesbetween 0.785 and 0.856. We further show the results ofgray-white matter segmentation overlaid on thehigh-resolution gray-scale images. The results arevisually checked for accuracy using the same principlesas commonly accepted in adult neuroimaging. Preliminary3D cortical reconstructions of the fetal brain are shownin Figure 2. Conclusion. We hereby present a completepipeline for the automated extraction of accuratethree-dimensional cortical surface of the fetal brain.These results are preliminary but promising, with theultimate goal to provide âeurooemovieâeuro of the normal gyraldevelopment. In turn, a precise knowledge of the normalfetal brain development will allow the quantification ofsubtle and early but clinically relevant deviations.Moreover, a precise understanding of the gyraldevelopment process may help to build hypotheses tounderstand the pathogenesis of several neurodevelopmentalconditions in which gyrification have been shown to bealtered (e.g. schizophrenia, autismâeuro¦). References.Rousseau, F. (2006), 'Registration-Based Approach forReconstruction of High-Resolution In Utero Fetal MR Brainimages', IEEE Transactions on Medical Imaging, vol. 13,no. 9, pp. 1072-1081. Jiang, S. (2007), 'MRI of MovingSubjects Using Multislice Snapshot Images With VolumeReconstruction (SVR): Application to Fetal, Neonatal, andAdult Brain Studies', IEEE Transactions on MedicalImaging, vol. 26, no. 7, pp. 967-980. Lee, S. (1997),'Scattered data interpolation with multilevel B-splines',IEEE Transactions on Visualization and Computer Graphics,vol. 3, no. 3, pp. 228-244. Bach Cuadra, M. (2010),'Central and Cortical Gray Mater Segmentation of MagneticResonance Images of the Fetal Brain', ISMRM Conference.Bach Cuadra, M. (2009), 'Brain tissue segmentation offetal MR images', MICCAI.

Second-order processes driven by dichotomous noise

We study free second-order processes driven by dichotomous noise. We obtain an exact differential equation for the marginal density p(x,t) of the position. It is also found that both the velocity ¿(t) and the position X(t) are Gaussian random variables for large t.

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.

Free inertial processes driven by Gaussian noise: Probability distributions, anomalous diffusion and fractal behavior

We study the motion of an unbound particle under the influence of a random force modeled as Gaussian colored noise with an arbitrary correlation function. We derive exact equations for the joint and marginal probability density functions and find the associated solutions. We analyze in detail anomalous diffusion behaviors along with the fractal structure of the trajectories of the particle and explore possible connections between dynamical exponents of the variance and the fractal dimension of the trajectories.

Integrated random processes exhibiting long tails, finite moments, and power-law spectra

A dynamical model based on a continuous addition of colored shot noises is presented. The resulting process is colored and non-Gaussian. A general expression for the characteristic function of the process is obtained, which, after a scaling assumption, takes on a form that is the basis of the results derived in the rest of the paper. One of these is an expansion for the cumulants, which are all finite, subject to mild conditions on the functions defining the process. This is in contrast with the Lévy distribution¿which can be obtained from our model in certain limits¿which has no finite moments. The evaluation of the spectral density and the form of the probability density function in the tails of the distribution shows that the model exhibits a power-law spectrum and long tails in a natural way. A careful analysis of the characteristic function shows that it may be separated into a part representing a Lévy process together with another part representing the deviation of our model from the Lévy process. This

Extreme times for volatility processes

Extreme times techniques, generally applied to nonequilibrium statistical mechanical processes, are also useful for a better understanding of financial markets. We present a detailed study on the mean first-passage time for the volatility of return time series. The empirical results extracted from daily data of major indices seem to follow the same law regardless of the kind of index thus suggesting an universal pattern. The empirical mean first-passage time to a certain level L is fairly different from that of the Wiener process showing a dissimilar behavior depending on whether L is higher or lower than the average volatility. All of this indicates a more complex dynamics in which a reverting force drives volatility toward its mean value. We thus present the mean first-passage time expressions of the most common stochastic volatility models whose approach is comparable to the random diffusion description. We discuss asymptotic approximations of these models and confront them to empirical results with a good agreement with the exponential Ornstein-Uhlenbeck model.

Estimation of jump-diffusion processes via empirical characteristic functions

Preface The starting point for this work and eventually the subject of the whole thesis was the question: how to estimate parameters of the affine stochastic volatility jump-diffusion models. These models are very important for contingent claim pricing. Their major advantage, availability T of analytical solutions for characteristic functions, made them the models of choice for many theoretical constructions and practical applications. At the same time, estimation of parameters of stochastic volatility jump-diffusion models is not a straightforward task. The problem is coming from the variance process, which is non-observable. There are several estimation methodologies that deal with estimation problems of latent variables. One appeared to be particularly interesting. It proposes the estimator that in contrast to the other methods requires neither discretization nor simulation of the process: the Continuous Empirical Characteristic function estimator (EGF) based on the unconditional characteristic function. However, the procedure was derived only for the stochastic volatility models without jumps. Thus, it has become the subject of my research. This thesis consists of three parts. Each one is written as independent and self contained article. At the same time, questions that are answered by the second and third parts of this Work arise naturally from the issues investigated and results obtained in the first one. The first chapter is the theoretical foundation of the thesis. It proposes an estimation procedure for the stochastic volatility models with jumps both in the asset price and variance processes. The estimation procedure is based on the joint unconditional characteristic function for the stochastic process. The major analytical result of this part as well as of the whole thesis is the closed form expression for the joint unconditional characteristic function for the stochastic volatility jump-diffusion models. The empirical part of the chapter suggests that besides a stochastic volatility, jumps both in the mean and the volatility equation are relevant for modelling returns of the S&P500 index, which has been chosen as a general representative of the stock asset class. Hence, the next question is: what jump process to use to model returns of the S&P500. The decision about the jump process in the framework of the affine jump- diffusion models boils down to defining the intensity of the compound Poisson process, a constant or some function of state variables, and to choosing the distribution of the jump size. While the jump in the variance process is usually assumed to be exponential, there are at least three distributions of the jump size which are currently used for the asset log-prices: normal, exponential and double exponential. The second part of this thesis shows that normal jumps in the asset log-returns should be used if we are to model S&P500 index by a stochastic volatility jump-diffusion model. This is a surprising result. Exponential distribution has fatter tails and for this reason either exponential or double exponential jump size was expected to provide the best it of the stochastic volatility jump-diffusion models to the data. The idea of testing the efficiency of the Continuous ECF estimator on the simulated data has already appeared when the first estimation results of the first chapter were obtained. In the absence of a benchmark or any ground for comparison it is unreasonable to be sure that our parameter estimates and the true parameters of the models coincide. The conclusion of the second chapter provides one more reason to do that kind of test. Thus, the third part of this thesis concentrates on the estimation of parameters of stochastic volatility jump- diffusion models on the basis of the asset price time-series simulated from various "true" parameter sets. The goal is to show that the Continuous ECF estimator based on the joint unconditional characteristic function is capable of finding the true parameters. And, the third chapter proves that our estimator indeed has the ability to do so. Once it is clear that the Continuous ECF estimator based on the unconditional characteristic function is working, the next question does not wait to appear. The question is whether the computation effort can be reduced without affecting the efficiency of the estimator, or whether the efficiency of the estimator can be improved without dramatically increasing the computational burden. The efficiency of the Continuous ECF estimator depends on the number of dimensions of the joint unconditional characteristic function which is used for its construction. Theoretically, the more dimensions there are, the more efficient is the estimation procedure. In practice, however, this relationship is not so straightforward due to the increasing computational difficulties. The second chapter, for example, in addition to the choice of the jump process, discusses the possibility of using the marginal, i.e. one-dimensional, unconditional characteristic function in the estimation instead of the joint, bi-dimensional, unconditional characteristic function. As result, the preference for one or the other depends on the model to be estimated. Thus, the computational effort can be reduced in some cases without affecting the efficiency of the estimator. The improvement of the estimator s efficiency by increasing its dimensionality faces more difficulties. The third chapter of this thesis, in addition to what was discussed above, compares the performance of the estimators with bi- and three-dimensional unconditional characteristic functions on the simulated data. It shows that the theoretical efficiency of the Continuous ECF estimator based on the three-dimensional unconditional characteristic function is not attainable in practice, at least for the moment, due to the limitations on the computer power and optimization toolboxes available to the general public. Thus, the Continuous ECF estimator based on the joint, bi-dimensional, unconditional characteristic function has all the reasons to exist and to be used for the estimation of parameters of the stochastic volatility jump-diffusion models.

A comparison of the processes of institutionalisation of political economy in Spain and Italy (1860-1900)

[spa] El estudio de los procesos a través de los cuales la economía política se ha transformado en una disciplina académica es un área de creciente interés en la historia del pensamiento económico. Dicho estudio se ha abordado a través del análisis de la importancia de la economía política en un conjunto de instituciones, consideradas clave en la expansión de la economía en las sociedades occidentales en la segunda mitad del siglo XIX y primeras décadas del XX: universidades, sociedades económicas, publicaciones periódicas de contenido económico y los parlamentos nacionales. Este papel presenta una comparación entre los desarrollos del proceso de institutionalización de la economía política en España e Italia, a través del estudio de la presencia de esta disciplina en las instituciones mencionadas para el periodo 1860-1900. El objetivo es medir la posible existencia de una vía común en la institucionalización de la economía política en ambos países, como un primer paso hacia la elaboración de un modelo supranacional de institucionalización de la economía en este periodo.

Why Italy and not Spain?: comparing two industrialization processes from a dissagregate time-series perspective

This study presents new evidence concerning the uneven processes of industrialization innineteenth century Spain and Italy based on a disaggregate analysis of the productivesectors from which the behaviour of the aggregate indices is comprised. The use of multivariate time-series analysis techniques can aid our understanding and characterization of these two processes of industrialization. The identification of those sectors with key rolesin leading industrial growth provides new evidence concerning the factors that governed thebehaviour of the aggregates in the two economies. In addition, the analysis of the existenceof interindustry linkages reveals the scale of the industrialization process, and wheresignificant differences exist, accounts for many of the divergences recorded in the historiography for the period 1850-1913.