Existence and Besov regularity of the density for a class of SDEs with Volterra noise

By using a simple method based on the fractional integration by parts, we prove the existence and the Besov regularity of the density for solutions to stochastic differential equations driven by an additive Gaussian Volterra process. We assume weak regularity conditions on the drift. Several examples of Gaussian Volterra noises are discussed.     

Asymptotic expansion for vector-valued sequences of random variables with focus on Wiener chaos

We develop the asymptotic expansion theory for vector-valued sequences ${\left(F_N\right)}_{N\ge 1}$ of random variables in terms of the convergence of the Stein–Malliavin matrix associated with the sequence $F_N$. Our approach combines the classical Fourier approach and the recent Stein–Malliavin theory. We find the second order term of the asymptotic expansion of the density of $F_N$ and we illustrate our results by several examples.     

SPDE with generalized drift and fractional-type noise

We consider a stochastic partial differential equation involving a second order differential operator whose drift is discontinuous. The equation is driven by a Gaussian noise which behaves as a Wiener process in space and the time covariance generates a signed measure. This class includes the Brownian motion, fractional Brownian motion and other related processes. We give a necessary and sufficient condition for the existence of the solution and we study the path regularity of this solution.     

On Planar Toeplitz Graphs

We describe several classes of finite, planar Toeplitz graphs and present results on their chromatic number. We then turn to counting maximal independent sets in these graphs and determine recurrence equations and generating functions for some special cases.     

Obtaining and characterizing modified tannins by physical-chemical methods

After oxidation of tannins (Tannins 1–3) extracted from grape seeds, Tanoxil compounds with increased solubility and enhanced antioxidant activities were synthesized. In this research, ABTS^+· assay and a chemiluminescence method were used for antioxidant measurement of hydrophilic compounds (Tanoxils 1–3).

It was observed that the antioxidant activity (AA, %) is very similar for the three samples, while at the same time AA is quite high (93.16%–96.48%). The percentage of inhibition by ABTS^+· is higher for Tanoxil 2 (96.4%) as compared to Tannin 2 compound (14.34%). Moreover, the total content (T_CF) of carboxyl and phenolic groups was investigated. T_CF values, determined for Tanoxil products, revealed a double (Tanoxil 1) or triple (Tanoxil 2) increase as compared to the value of the T_CF of Tannin 1. Tanoxil products represent an interest for future research as they have a high AA (96.4%) and the content of acidic groups is significant (T_CF, 0.191 meq g^?1).

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