This paper is devoted to a factorization of the higher dimensional Schrodinger operator in the framework of Clifford analysis.

Nele De Schepper Dixan Peña Peña

We study the self-normalized sums of independent random variables from the perspective of the Malliavin calculus. We give the chaotic expansion for them and we prove a Berry-Ess\'een bound with respect to several distances.

Solesne Bourguin Ciprian Tudor

For an Ornstein-Uhlenbeck process driven by a fractional Brownian motion with Hurst parameter 0<H<1/2, one shows the Berry-Ess\'een bound of the least squares estimator of the drift parameter. Thus, a problem left in the previous paper (Chen, Kuang and Li in Stochastics and Dynamics, 2019+) is solved, where the Berry-Ess\'een bound of the least squares estimator is proved for 1/2<=H<=3/4. An approach based on Malliavin calculus given by Kim and Park \cite{kim 3} is used

Yong Chen Nenghui Kuang

A complete characterization of the asymptotic singularity probability of random circulant Bernoulli matrices is given for all values of the probability parameter.

Niklas Miller

The structural symmetry of forty-three face-on galaxy images in the R(65 0 nm) and J(450 nm) bands are measured to determine the usefulness of symmetry a s a morphological parameter. Each galaxy image is rotated by $180$\deg and subtr acted from the original to obtain a quantitative value for its structural symmet ry. The symmetry numbers computed for the sample are then compared with RC3 mor phological types, color \& absolute blue magnitudes. A strong correlation betw een color and symmetry is found, and the RC3 Hubble sequence is found to be one of increasing asymmetry. The use of symmetry as a morphological parameter, and the possible causes of the asymmetries are discussed.

Christopher J. Conselice

We combine Stein's method with a version of Malliavin calculus on the Poisson space. As a result, we obtain explicit Berry-Ess\'een bounds in Central Limit Theorems (CLTs) involving multiple Wiener-It\^o integrals with respect to a general Poisson measure. We provide several applications to CLTs related to Ornstein-Uhlenbeck L\'evy processes.

Giovanni Peccati Josep Lluís Solé Murad S. Taqqu Frederic Utzet

We establish nearly optimal rates of convergence to self-similar solutions of Smoluchowski's coagulation equation with kernels $K = 2$, $x + y$, and $xy$. The method is a simple analogue of the Berry-Ess\'een theorem in classical probability and requires minimal assumptions on the initial data, namely that of an extra finite moment condition. For each kernel it is shown that the convergence rate is achieved in the case of monodisperse initial data.

Ravi Srinivasan

Let $B$ be a bifractional Brownian motion with parameters $H\in (0, 1)$ and $K\in(0,1]$. For any $n\geq1$, set $Z_n =\sum_{i=0}^{n-1}\big[n^{2HK}(B_{(i+1)/n}-B_{i/n})^2-\E((B_{i+1}-B_{i})^2)\big]$. We use the Malliavin calculus and the so-called Stein's method on Wiener chaos introduced by Nourdin and Peccati \cite{NP09} to derive, in the case when $0<HK\leq3/4$, Berry-Ess\'een-type bounds for the Kolmogorov distance between the law of the correct renormalization $V_n$ of $Z_n$ and the standard normal law. Finally, we study almost sure central limit theorems for the sequence $V_n$.

Soufiane Aazizi Khalifa Es-Sebaiy

In this paper, we investigate the general formulation for inextensible flows of curves in En. The necessary and sufficient conditions for inextensible curve flow are expressed as a partial differential equation involving the curvatures.

Önder Gökmen Yıldız Murat Tosun Sıddıka Ö. Karakuş

We give a simple technic to derive the Berry-Ess\'een bounds for the quadratic variation of the subfractional Brownian motion (subfBm). Our approach has two main ingredients: ($i$) bounding from above the covariance of quadratic variation of subfBm by the covariance of the quadratic variation of fractional Brownian motion (fBm); and ($ii$) using the existing results on fBm in \cite{BN08,NP09,N12}. As a result, we obtain simple and direct proof to derive the rate of convergence of quadratic variation of subfBm. In addition, we also improve this rate of convergence to meet the one of fractional Brownian motion in \cite{N12}.

Soufiane Aazizi