Intenzitásalapú modellezés és a mértékcsere (Intensity-based modeling and thje change of measure)

A dolgozatban a hitelderivatívák intenzitásalapú modellezésének néhány kérdését vizsgáljuk meg. Megmutatjuk, hogy alkalmas mértékcserével nemcsak a duplán sztochasztikus folyamatok, hanem tetszőleges intenzitással rendelkező pontfolyamat esetén is kiszámolható az összetett kár- és csődfolyamat eloszlásának Laplace-transzformáltja. _____ The paper addresses questions concerning the use of intensity based modeling in the pricing of credit derivatives. As the specification of the distribution of the lossprocess is a non-trivial exercise, the well-know technique for this task utilizes the inversion of the Laplace-transform. A popular choice for the model is the class of doubly stochastic processes given that their Laplace-transforms can be determined easily. Unfortunately these processes lack several key features supported by the empirical observations, e.g. they cannot replicate the self-exciting nature of defaults. The aim of the paper is to show that by using an appropriate change of measure the Laplace-transform can be calculated not only for a doubly stochastic process, but for an arbitrary point process with intensity as well. To support the application of the technique, we investigate the e®ect of the change of measure on the stochastic nature of the underlying process.

A coherent approach to non-integer order derivatives

Signal Processing, vol. 86, nº 10

Modelling and Control of Freeway Traffic

This paper presents the most recent developments of the Simulator of Intelligent Transportation Systems (SITS). The SITS is based on a microscopic simulation approach to reproduce real traffic conditions in an urban or non-urban network. In order to analyse the quality of the microscopic traffic simulator SITS a benchmark test was performed. A dynamical analysis of several traffic phenomena, applying a new modelling formalism based on the embedding of statistics and Laplace transform, is then addressed. The paper presents also a new traffic control concept applied to a freeway traffic system.

On the analysis of data emerging in non-linear and complex systemscomparison of two X-Ray prony spectra

New arguments proving that successive (repeated) measurements have a memory and actually remember each other are presented. The recognition of this peculiarity can change essentially the existing paradigm associated with conventional observation in behavior of different complex systems and lead towards the application of an intermediate model (IM). This IM can provide a very accurate fit of the measured data in terms of the Prony's decomposition. This decomposition, in turn, contains a small set of the fitting parameters relatively to the number of initial data points and allows comparing the measured data in cases where the “best fit” model based on some specific physical principles is absent. As an example, we consider two X-ray diffractometers (defined in paper as A- (“cheap”) and B- (“expensive”) that are used after their proper calibration for the measuring of the same substance (corundum a-Al2O3). The amplitude-frequency response (AFR) obtained in the frame of the Prony's decomposition can be used for comparison of the spectra recorded from (A) and (B) - X-ray diffractometers (XRDs) for calibration and other practical purposes. We prove also that the Fourier decomposition can be adapted to “ideal” experiment without memory while the Prony's decomposition corresponds to real measurement and can be fitted in the frame of the IM in this case. New statistical parameters describing the properties of experimental equipment (irrespective to their internal “filling”) are found. The suggested approach is rather general and can be used for calibration and comparison of different complex dynamical systems in practical purposes.

Improved multiexponential transient spectroscopy by iterative deconvolution

The analysis of multiexponential decays is challenging because of their complex nature. When analyzing these signals, not only the parameters, but also the orders of the models, have to be estimated. We present an improved spectroscopic technique specially suited for this purpose. The proposed algorithm combines an iterative linear filter with an iterative deconvolution method. A thorough analysis of the noise effect is presented. The performance is tested with synthetic and experimental data.

Reconstruction and analysis of surface variation using photometric stereo

In many industrial applications, accurate and fast surface reconstruction is essential for quality control. Variation in surface finishing parameters, such as surface roughness, can reflect defects in a manufacturing process, non-optimal product operational efficiency, and reduced life expectancy of the product. This thesis considers reconstruction and analysis of high-frequency variation, that is roughness, on planar surfaces. Standard roughness measures in industry are calculated from surface topography. A fast and non-contact method to obtain surface topography is to apply photometric stereo in the estimation of surface gradients and to reconstruct the surface by integrating the gradient fields. Alternatively, visual methods, such as statistical measures, fractal dimension and distance transforms, can be used to characterize surface roughness directly from gray-scale images. In this thesis, the accuracy of distance transforms, statistical measures, and fractal dimension are evaluated in the estimation of surface roughness from gray-scale images and topographies. The results are contrasted to standard industry roughness measures. In distance transforms, the key idea is that distance values calculated along a highly varying surface are greater than distances calculated along a smoother surface. Statistical measures and fractal dimension are common surface roughness measures. In the experiments, skewness and variance of brightness distribution, fractal dimension, and distance transforms exhibited strong linear correlations to standard industry roughness measures. One of the key strengths of photometric stereo method is the acquisition of higher frequency variation of surfaces. In this thesis, the reconstruction of planar high-frequency varying surfaces is studied in the presence of imaging noise and blur. Two Wiener filterbased methods are proposed of which one is optimal in the sense of surface power spectral density given the spectral properties of the imaging noise and blur. Experiments show that the proposed methods preserve the inherent high-frequency variation in the reconstructed surfaces, whereas traditional reconstruction methods typically handle incorrect measurements by smoothing, which dampens the high-frequency variation.

Retrial Queues with Orbital Search

Queueing system in which arriving customers who find all servers and waiting positions (if any) occupied many retry for service after a period of time are retrial queues or queues with repeated attempts. This study deals with two objectives one is to introduce orbital search in retrial queueing models which allows to minimize the idle time of the server. If the holding costs and cost of using the search of customers will be introduced, the results we obtained can be used for the optimal tuning of the parameters of the search mechanism. The second one is to provide insight of the link between the corresponding retrial queue and the classical queue. At the end we observe that when the search probability Pj = 1 for all j, the model reduces to the classical queue and when Pj = 0 for all j, the model becomes the retrial queue. It discusses the performance evaluation of single-server retrial queue. It was determined by using Poisson process. Then it discuss the structure of the busy period and its analysis interms of Laplace transforms and also provides a direct method of evaluation for the first and second moments of the busy period. Then it discusses the M/ PH/1 retrial queue with disaster to the unit in service and orbital search, and a multi-server retrial queueing model (MAP/M/c) with search of customers from the orbit. MAP is convenient tool to model both renewal and non-renewal arrivals. Finally the present model deals with back and forth movement between classical queue and retrial queue. In this model when orbit size increases, retrial rate also correspondingly increases thereby reducing the idle time of the server between services

“Improved Feature Extraction and Classification Techniques for Multispectral Brain Magnetic Resonance Images”

Magnetic Resonance Imaging (MRI) is a multi sequence medical imaging technique in which stacks of images are acquired with different tissue contrasts. Simultaneous observation and quantitative analysis of normal brain tissues and small abnormalities from these large numbers of different sequences is a great challenge in clinical applications. Multispectral MRI analysis can simplify the job considerably by combining unlimited number of available co-registered sequences in a single suite. However, poor performance of the multispectral system with conventional image classification and segmentation methods makes it inappropriate for clinical analysis. Recent works in multispectral brain MRI analysis attempted to resolve this issue by improved feature extraction approaches, such as transform based methods, fuzzy approaches, algebraic techniques and so forth. Transform based feature extraction methods like Independent Component Analysis (ICA) and its extensions have been effectively used in recent studies to improve the performance of multispectral brain MRI analysis. However, these global transforms were found to be inefficient and inconsistent in identifying less frequently occurred features like small lesions, from large amount of MR data. The present thesis focuses on the improvement in ICA based feature extraction techniques to enhance the performance of multispectral brain MRI analysis. Methods using spectral clustering and wavelet transforms are proposed to resolve the inefficiency of ICA in identifying small abnormalities, and problems due to ICA over-completeness. Effectiveness of the new methods in brain tissue classification and segmentation is confirmed by a detailed quantitative and qualitative analysis with synthetic and clinical, normal and abnormal, data. In comparison to conventional classification techniques, proposed algorithms provide better performance in classification of normal brain tissues and significant small abnormalities.

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