Functional Limit Theorems for Multiparameter Fractional Brownian Motion

We prove a general functional limit theorem for multiparameter fractional Brownian motion. The functional law of the iterated logarithm, functional Lévy’s modulus of continuity and many other results are its particular cases. Applications to approximation theory are discussed.      

Numerical Studies on Asymptotics of European Option Under Multiscale Stochastic Volatility

Multiscale stochastic volatilities models relax the constant volatility assumption from Black-Scholes option pricing model. Such models can capture the smile and skew of volatilities and therefore describe more accurately the movements of the trading prices. Christoffersen et al. Manag Sci 55(2):1914–1932 (2009) presented a model where the underlying price is governed by two volatility components, one changing fast and another changing slowly. Chiarella and Ziveyi Appl Math Comput 224:283–310 (2013) transformed Christoffersen’s model and computed an approximate formula for pricing American options. They used Duhamel’s principle to derive an integral form solution of the boundary value problem associated to the option price. Using method of characteristics, Fourier and Laplace transforms, they obtained with good accuracy the American option prices. In a previous research of the authors (Canhanga et al. 2014), a particular case of Chiarella and Ziveyi Appl Math Comput 224:283–310 (2013) model is used for pricing of European options. The novelty of this earlier work is to present an asymptotic expansion for the option price. The present paper provides experimental and numerical studies on investigating the accuracy of the approximation formulae given by this asymptotic expansion. We present also a procedure for calibrating the parameters produced by our first-order asymptotic approximation formulae. Our approximated option prices will be compared to the approximation obtained by Chiarella and Ziveyi Appl Math Comput 224:283–310 (2013).     

An Optimal Series Expansion of the Multiparameter Fractional Brownian Motion

We derive a series expansion for the multiparameter fractional Brownian motion. The derived expansion is proven to be rate optimal. This work is supported in part by the Foundation for Knowledge and Competence Development and Sparbanksstiftelsen Nya.     

Spin transistor and quantum spin Hall-effects in CdBxF2−x–p-CdF2–CdBxF2−x sandwich nanostructures

Planar CdB_xF_2−x–p-CdF₂–CdB_xF_2−x sandwich nanostructures prepared on the surface of the n-type CdF₂ bulk crystal are studied to register the spin transistor and quantum spin Hall-effects. The current–voltage characteristics of the ultra-shallow p⁺–n junctions verify the CdF₂ gap, 7.8 eV, and the quantum subbands of the 2D holes in the p-type CdF₂ quantum well confined by the CdB_xF_2−xδ-barriers. The temperature and magnetic field dependencies of the resistance, specific heat and magnetic susceptibility demonstrate the high temperature superconductor properties for the CdB_xF_2−xδ-barriers. The value of the superconductor energy gap, 2Δ = 102.06 meV, determined by the tunneling spectroscopy method appears to be in a good agreement with the relationship between the zero-resistance supercurrent in superconductor state and the conductance in normal state, πΔ/e, at the energies of the 2D hole subbands. The results obtained are evidence of the important role of the multiple Andreev reflections in the creation of the high spin polarization of the 2D holes in the edged channels of the sandwich device. The high spin hole polarization in the edged channels is shown to identify the mechanism of the spin transistor and quantum spin Hall-effects induced by varying the top gate voltage, which is revealed by the first observation of the Hall quantum conductance staircase.     

EDESR and ODMR of Impurity Centers in Nanostructures Inserted in Silicon Microcavities

We present the first findings of the new electrically and optically detected magnetic resonance technique [ED electron spin resonance (EDESR) and ODMR], which reveal single point defects in the ultra-narrow silicon quantum wells (Si-QW) confined by the superconductor δ-barriers. This technique allows the ESR identification without application of an external cavity, as well as a high frequency source and recorder, and with measuring only the magnetoresistance (EDESR) and transmission (ODMR) spectra within the frameworks of the excitonic normal-mode coupling caused by the microcavities embedded in the Si-QW plane. The new resonant positive magnetoresistance data are interpreted here in terms of the interference transition in the diffusive transport of free holes, respectively, between the weak antilocalization regime in the region far from the ESR of a paramagnetic point defect located inside or near the conductive channel and the weak localization regime in the nearest region of the ESR of that defect.     

A Random Field Formulation of Hooke’s Law in All Elasticity Classes

For each of the 8 symmetry classes of elastic materials, we consider a homogeneous random field taking values in the fixed point set \(\mathsf {V}\) of the corresponding class, that is isotropic with respect to the natural orthogonal representation of a group lying between the isotropy group of the class and its normaliser. We find the general form of the correlation tensors of orders 1 and 2 of such a field, and the field’s spectral expansion.     

Deconvolution filters to enhance resolution of dense time-of-flight survey spectra in the time-lag optimization range

By applying time-domain filters to time-of-flight (TOF) mass spectrometry signals, we have simultaneously smoothed and narrowed spectra resulting in improved resolution and increased signal-to-noise ratios. This filtering procedure has an advantage over detailed curve fitting of spectra in the case of large dense spectra, when neither the location nor the number of mass peaks is known a priori. This time series method is directly applicable in the time lag optimization range, where point density per peak is constant. We present a systematic methodology to optimize the filters according to any desired figure of merit, illustrating the procedure by optimizing the signal-to-noise per unit bandwidth of matrix-assisted laser desorption/ionization (MALDI) data. We also introduce a nonlinear filter that reduces the spurious structure that often accompanies deconvolution filters. The net result of the application of these filters is that we can identify new structures in dense MALDI-TOF data, clearly showing small adducts to heavy biomolecules.     

Matérn Class Tensor-Valued Random Fields and Beyond

We construct classes of homogeneous random fields on a three-dimensional Euclidean space that take values in linear spaces of tensors of a fixed rank and are isotropic with respect to a fixed orthogonal representation of the group of \(3\times 3\) orthogonal matrices. The constructed classes depend on finitely many isotropic spectral densities. We say that such a field belongs to either the Matérn or the dual Matérn class if all of the above densities are Matérn or dual Matérn. Several examples are considered.     

Automated assignment of ionization states in broad‐mass matrix‐assisted laser desorption/ionization spectra of protein mixtures

A computational technique is presented for the automated assignment of the multiple charge and multimer states (ionization states) in the time‐of‐flight (TOF) domain for matrix‐assisted laser desorption/ionization (MALDI) spectra. Examples of the application of this technique include an improved, automatic calibration over the 2 to 70 kDa mass range and a reduced data redundancy after reconstruction of the molecular spectrum of only singly charged monomers. This method builds on our previously reported enhancement of broad‐mass signal detection, and includes two steps: (1) an automated correction of the instrumental acquisition initial time delay, and (2) a recursive TOF detection of multiple charge states and singly charged multimers of molecular [MH]⁺ ions over the entire record range, based on MALDI methods. The technique is tested using calibration mixtures and pooled serum quality control samples acquired along with clinical study data. The described automated procedure improves the analysis and dimension reduction of MS data for comparative proteomics applications. Copyright © 2009 John Wiley & Sons, Ltd.