29 research outputs found

    Free area estimation in a partially observed dynamic germ-grain model

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    The estimation problem of the expected local fraction of free area function S for a partially observed dynamic germ-grain model is presented. Properties of the estimators are proved by martingale and product integral methods. Confidence bounds are provided. Furthermore, an estimator of the hazard rate α(t)=−dS(t)/(S(t)dt) is obtained by the kernel function method and asymptotic properties of the estimator are proved and used to find confidence intervals. By a simulated illustrative example, the qualitative behavior of the estimators is shown

    Forecasting interest rates through Vasicek and CIR models: a partitioning approach

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    The aim of this paper is to propose a new methodology that allows forecasting, through Vasicek and CIR models, of future expected interest rates (for each maturity) based on rolling windows from observed financial market data. The novelty, apart from the use of those models not for pricing but for forecasting the expected rates at a given maturity, consists in an appropriate partitioning of the data sample. This allows capturing all the statistically significant time changes in volatility of interest rates, thus giving an account of jumps in market dynamics. The performance of the new approach is carried out for different term structures and is tested for both models. It is shown how the proposed methodology overcomes both the usual challenges (e.g. simulating regime switching, volatility clustering, skewed tails, etc.) as well as the new ones added by the current market environment characterized by low to negative interest rates.Comment: Research artcile, 23 pages, 8 figures, 7 table

    Applications of PDEs inpainting to magnetic particle imaging and corneal topography

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    In this work we propose a novel application of Partial Differential Equations (PDEs) inpainting techniques to two medical contexts. The first one concerning recovering of concentration maps for superparamagnetic nanoparticles, used as tracers in the framework of Magnetic Particle Imaging. The analysis is carried out by two set of simulations, with and without adding a source of noise, to show that the inpainted images preserve the main properties of the original ones. The second medical application is related to recovering data of corneal elevation maps in ophthalmology. A new procedure consisting in applying the PDEs inpainting techniques to the radial curvature image is proposed. The images of the anterior corneal surface are properly recovered to obtain an approximation error of the required precision. We compare inpainting methods based on second, third and fourth-order PDEs with standard approximation and interpolation techniques

    Higher-order Cahn–Hilliard equations with dynamic boundary conditions

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    Our aim in this paper is to study the well-posedness and the dissipativity of higher-order Cahn–Hilliard equations with dynamic boundary conditions. More precisely, we prove the existence and uniqueness of solutions and the existence of the global attractor
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