Estimation of integrated volatility in stochastic volatility models

In the framework of stochastic volatility models we examine estimators for the integrated volatility based on the pth power variation (i.e. the sum of pth absolute powers of the log‐returns). We derive consistency and distributional results for the estimators given high‐frequency data, especially taking into account what kind of process we may add to our model without affecting the estimate of the integrated volatility. This may on the one hand be interpreted as a possible flexibility in modelling, for example adding jumps or even leaving the framework of semimartingales by adding a fractional Brownian motion, or on the other hand as robustness against model misspecification. We will discuss possible choices of p under different model assumptions and irregularly spaced data. Copyright © 2005 John Wiley & Sons, Ltd.     

Vector-Orthogonality and Lanczos-Type Methods

A method for solving a linear system is defined. It is a Lanczos-type method, but it uses formal vector orthogonality instead of scalar orthogonality. Moreover, the dimension of vector orthogonality may vary which gives a large freedom in leading the algorithm, and controlling the numerical problems. The ideas of truncated and restarted methods are revisited. The obtained residuals are exactly orthogonal to a space of increasing dimension. Some experiments are done, the problem of finding automaticaly good directions of projection remains partly open.     

GnRH binding RNA and DNA Spiegelmers: a novel approach toward GnRH antagonism

Mirror-image oligonucleotide ligands (Spiegelmers) that bind to the pharmacologically relevant target gonadotropin-releasing hormone I (GnRH) with high affinity and high specificity have been identified using the Spiegelmer technology. GnRH is a decapeptide that plays an important role in mammalian reproduction and sexual maturation and is associated with several benign and malignant diseases. First, aptamers that bind to D-GnRH with dissociation constants of 50-100 nM were isolated out of RNA and DNA libraries. The respective enantiomers of the DNA and RNA aptamers were synthesized, and their binding to L-GnRH was shown. These Spiegelmers bind to L-GnRH with similar affinity to that of the corresponding aptamers that bind to D-GnRH. We further demonstrated dose-dependent inhibition of GnRH-induced Ca(2+) release in Chinese hamster ovary cells that were stably transfected with the human GnRH receptor.     

Preparation and spectroscopic properties of 2-benzothiazolyl araldehyde hydrazones

Notwithstanding its tendency toward air oxidation in solution, 2-hydrazinobenzothiazole I reacted with aromatic aldehydes in ethanol to give the corresponding hydrazones III-XV in high yields and analytical purity. In related examples, acylation took place under similar conditions to produce hydrazides XVI-XX . The near-infrared bands of the absorption spectra of the araldehyde hydrazones have been associated with charge transfer and appeared to correlate with structural elements of the compounds in a way suggesting that the charge transfer was intermolecular.     

On the use of x-ray-excited optical luminescence (XEOL) for the analysis of multisite rare-earth systems

The realization of a XEOL (X-ray-excited optical luminescence) spectrometer is reported. The aim of the present paper is to show that a comparison between UV-excited emission spectra and XEOL spectra can be helpful in the assignment of some weak transitions for multiple site rare-earth compounds. The case of c-Y₂O₃ doped with Eu³⁺ cations is considered in some detail, as in the XEOL spectrum three lines to be assigned to transitions occurring at the centrosymmetrical Eu³⁺ (C_3i) site are strongly enhanced. Additional site-selective UV-excited emission spectra are also reported supporting the present discussion.     

On a site-selective exafs experiment using optical emission

X-ray-excited optical luminescence (XEOL) is known to offer an alternative detection scheme of EXAFS spectra. Although this secondary emission appears restricted to a rather limited number of systems, we show that it can afford, under appropriate circumstances, an interesting property of site selectivity. The case of a ZnO + ZnTPP mixture was chosen as an illustrative example. The relevant formulation of the phenomenon for powdered samples is developed and the requirements for site selectivity are discussed.     

Matrix Continued Fraction for the Resolvent Function of the Band Operator

The aim of this paper is the expansion of a matrix function in terms of a matrix-continued fraction as defined by Sorokin and Van Iseghem. The function under study is the Weyl function or resolvent function of an operator, given in the standard basis by a bi-infinite band matrix, with p subdiagonals and q superdiagonals, where the p + q – 1 intermediate diagonals are zero. The main goal of this paper is to find, for the moments, an explicit form in terms of the coefficients of the continued fraction, called genetic sums, which lead to a generalization of the notion of a Stieltjes continued fraction. These results are extension of some results already found for the vector case (p = 1) and are a step in the direction towards the solution of the direct and inverse spectral problem. The actual computation of the approximants of the given function as the convergents of the continued fraction is shown to be effective. Some possible extensions are considered.     

Matrix characterization of oscillation for double sequences

The notion of oscillation for ordinary sequences was presented by Hurwitz in 1930. Using this notion Agnew and Hurwitz presented regular matrix characterization of the resulting sequence space. The primary goal of this article is to extend this definition to double sequences, which grants us the following definition: the double oscillation of a double sequence of real or complex number is given P-lim sup_{(m,n)→∞;(α,β)→∞}|S _m,n -S _α,β |. Using this concept a matrix characterization of double oscillation sequence space is presented. Other implication and variation shall also be presented.