A bound on the Wasserstein-2 distance between linear combinations of independent random variables

We provide a bound on a distance between finitely supported elements and general elements of the unit sphere of ${?}^2\left({\mathbb{N}}^1\right)$. We use this bound to estimate the Wasserstein-2 distance between random variables represented by linear combinations of independent random variables. Our results are expressed in terms of a discrepancy measure related to Nourdin–Peccati’s Malliavin–Stein method. The main application is towards the computation of quantitative rates of convergence to elements of the second Wiener chaos. In particular, we explicit these rates for non-central asymptotic of sequences of quadratic forms and the behavior of the generalized Rosenblatt process at extreme critical exponent.     

Spectral characterization of the quadratic variation of mixed Brownian–fractional Brownian motion

Dzhaparidze and Spreij (Stoch Process Appl, 54:165–174, 1994) showed that the quadratic variation of a semimartingale can be approximated using a randomized periodogram. We show that the same approximation is valid for a special class of continuous stochastic processes. This class contains both semimartingales and non-semimartingales. The motivation comes partially from the recent work by Bender et al. (Finance Stoch, 12:441–468, 2008), where it is shown that the quadratic variation of the log-returns determines the hedging strategy.     

Synthesis,metal ion complexation and first use of a thia-aza substituted macrocyclic diamide as a novel sensing material for preparation of selective and sensitive poly(vinyl chloride)-membrane potentiometric sensors for Ag+ ion

A novel thia-aza substituted macrocyclic diamide 7,10,13-triaza-1-thia-4,16-dioxa-20,24-dimethyl-2,3;17,18-dibenzo-cyclooctadecane-6,14-dione (L) was synthesized and stability of its complexes with several alkaline earth, transition and heavy metal ions were studied conductometrically in methanol solution. The resulting 1:1 Ag⁺–L complex found to be the most stable one among all cation complexes studied. The optimized structures of the ligand and its Ag⁺ complex were also investigated. Based on the preliminary results thus obtained, L was used as an excellent sensing material to prepare polymeric membrane (PME) and coated graphite (CGE) silver-selective electrodes. The electrodes revealed a Nernstian behavior over wide Ag⁺ ion concentration ranges (i.e., 2.0 × 10^?6–1.0 × 10^?2 M for PME and 5.0 × 10^?7–1.0 × 10^?2 M for CGE). The potentiometric responses were independent of pH of the test solution in the range 2.9–6.8. The electrodes possessed advantages of low resistance, relatively fast response time, long lifetimes and, especially, good selectivity relative to a wide variety of other cations. The electrodes were used, as indicator electrodes, in the potentiometric titration of silver ion and in the determination of Ag⁺ ion in waste water, photographic emulsion, radiographic and photographic films and dental amalgams.     

How Does Tempering Affect the Local and Global Properties of Fractional Brownian Motion?

Journal of Theoretical Probability - The present paper investigates the effects of tempering the power law kernel of the moving average representation of a fractional Brownian motion (fBm) on some...     

Hollow fiber supported liquid membrane microextraction of Cu2+ followed by flame atomic absorption spectroscopy determination

Hollow fiber supported liquid membrane microextraction, a relatively new sample preparation technique, has attracted much interest in the field of environmental analysis. In the current study, a novel method based on hollow-fiber liquid-phase microextraction and flame atomic absorption spectrometry (FAAS) for the measurement of copper ion in aqueous samples is described. Hollow-fiber liquid-phase microextraction conditions such as the type of extraction solvent, pH, the stirring rate, and the amounts of chelating agents, sample volume, and the extraction time were investigated. Under the optimized conditions, the linear range was found to be 0.01–15 μg ml^?1 for copper ion, and the limit of detection to be 0.004 μg ml^?1. Tap water and surface water samples collected from Mashhad, Iran and Dorongar river; Khorasan, Iran, respectively, were successfully analyzed using the proposed method. The recoveries from the spiked water samples were 72.4% and 105%, respectively; and the relative standard deviation (RSD) at the 2 μg ml^?1 level was 6%.     

Fourth Moment Theorems for Markov diffusion generators

Inspired by the insightful article [4], we revisit the Nualart–Peccati criterion [13] (now known as the Fourth Moment Theorem) from the point of view of spectral theory of general Markov diffusion generators. We are not only able to drastically simplify all of its previous proofs, but also to provide new settings of diffusive generators (Laguerre, Jacobi) where such a criterion holds. Convergence towards Gamma and Beta distributions under moment conditions is also discussed.