Bipower-type estimation in a noisy diffusion setting

We consider a new class of estimators for volatility functionals in the setting of frequently observed Itō diffusions which are disturbed by i.i.d. noise. These statistics extend the approach of pre-averaging as a general method for the estimation of the integrated volatility in the presence of microstructure noise and are closely related to the original concept of bipower variation in the no-noise case. We show that this approach provides efficient estimators for a large class of integrated powers of volatility and prove the associated (stable) central limit theorems. In a more general Itō semimartingale framework this method can be used to define both estimators for the entire quadratic variation of the underlying process and jump-robust estimators which are consistent for various functionals of volatility. As a by-product we obtain a simple test for the presence of jumps in the underlying semimartingale.     

Fragmentation of the chain in the mass spectra of the pyrrolidides of alkylcyclohexanecarboxylic acids

The electron impact mass spectra of the pyrrolidides of both the cis- and trans-octylcyclohexanecarboxylic acids show the structure of the aliphatic chain, despite the steric hindrance of a direct H transfer from the chain to the functional group.     

Electric field gradients at (111)In/(111)Cd probe atoms on A-sites in 211-MAX phases

The method of perturbed angular correlation (PAC) was applied to selected MAX phases with 211 stoichiometry. Radioactive (111)In ions were implanted in order to measure the electric field gradients (EFG) in the key compounds Ti(2)InC and Zr(2)InC to determine the strength and symmetry of the EFG at the In-site. Further PAC studies in the In-free MAX phases Ti(2)AlN, Nb(2)AlC, Nb(2)AsC and Cr(2)GeC were performed to confirm that the In probes occupy the A-site as well. The strength of the EFG, with a quadrupole coupling constant ν(Q) between 250 and 300 MHz in these phases, is quite similar to the ones found in Ti(2)InC with ν(Q) = 292(1) MHz and in Zr(2)InC with ν(Q) = 344(1) MHz, respectively. Different annealing behavior was observed whereas in all cases a linear decrease of ν(Q) with increasing measuring temperatures was found. The experimental results are also in excellent agreement with those predicted by ab initio calculations using the APW+lo method implemented in the WIEN2k code. This study shows in an exceptional manner that (111)In?→?(111)Cd atoms are suitable probes to investigate the local surrounding at the A-site in 211-MAX phases.     

Eine einfache Schnellmethode zur Bestimmung der schwefligen S?ure in der Luft

Ohne Zusammenfassung     

Bemerkung zu dem Artikel Ein neuer elementarer Irrationalit?tsbeweis für π Math. Semesterber. 53:101–107 (2006)

Ohne Zusammenfassung The online version of the original article can be found at http://dx.doi.org/10.1007/s00591-005-0103-z     

A universal approach to estimate the conditional variance in semimartingale limit theorems

The typical central limit theorems in high-frequency asymptotics for semimartingales are results on stable convergence to a mixed normal limit with an unknown conditional variance. Estimating this conditional variance usually is a hard task, in particular when the underlying process contains jumps. For this reason, several authors have recently discussed methods to automatically estimate the conditional variance, i.e. they build a consistent estimator from the original statistics, but computed at different time scales. Their methods work in several situations, but are essentially restricted to the case of continuous paths always. The aim of this work is to present a new method to consistently estimate the conditional variance which works regardless of whether the underlying process is continuous or has jumps. We will discuss the case of power variations in detail and give insight to the heuristics behind the approach.