Statistical inference for Vasicek-type model driven by Hermite processes

Let $Z$ denote a Hermite process of order $q\ge 1$ and self-similarity parameter $H\in (\frac{1}{2},1)$. This process is $H$-self-similar, has stationary increments and exhibits long-range dependence. When $q=1$, it corresponds to the fractional Brownian motion, whereas it is not Gaussian as soon as $q?2$. In this paper, we deal with a Vasicek-type model driven by $Z$, of the form $d{X}_t=a(b?X_t)dt+d{Z}_t$. Here, $a>0$ and $b\in \mathbb{R}$ are considered as unknown drift parameters. We provide estimators for $a$ and $b$ based on continuous-time observations. For all possible values of $H$ and $q$, we prove strong consistency and we analyze the asymptotic fluctuations.     

An efficient iterative method for finding common fixed point and variational inequalities in Hilbert spaces

ABSTRACT

In this paper, we investigate the problem of finding a common solution to a fixed point problem involving demi-contractive operator and a variational inequality with monotone and Lipschitz continuous mapping in real Hilbert spaces. Inspired by the projection and contraction method and the hybrid descent approximation method, a new and efficient iterative method for solving the problem is introduced. Strong convergence theorem of the proposed method is established under standard and mild conditions. Our scheme generalizes and extends some of the existing results in the literature, and moreover, its computational effort is less per each iteration compared with related works.     

Approximation of Functions by the Szász-Mirakjan-Kantorovich Operator

We characterize the approximation of functions in the L_p-norm by the Szász-Mirakjan-Kantorovich operator. We prove a direct and a strong converse inequality of type B in terms of an appropriate K-functional.     

On local strong solutions to the Cauchy problem of the two-dimensional full compressible magnetohydrodynamic equations with vacuum and zero heat conduction

This paper concerns the Cauchy problem of the two-dimensional full compressible magnetohydrodynamic equations with zero heat-conduction and vacuum as far field density. In particular, the initial density can have compact support. We prove that the Cauchy problem admits a local strong solution provided both the initial density and the initial magnetic field decay not too slow at infinity.     

Existence and uniqueness of maximal strong solution of a 1D blood flow in a network of vessels

We study the well-posedness of a system of one-dimensional partial differential equations modeling blood flows in a network of vessels with viscoelastic walls. We prove the existence and uniqueness of maximal strong solution for this type of hyperbolic/parabolic model. We also prove a stability estimate under suitable nonlinear Robin boundary conditions.     

Optical spectra of organic quantum dots in the strong coupling regime

We analyze the emission spectrum of a single organic quantum dot coupled to a microcavity in the strong coupling regime. We take into account non-linearities arising from both exciton–exciton interactions and the Pauli exclusion principle. We apply the recently developed Pade approximation for regular truncation of Green functions to calculate the emission spectrum. We show that as the number of excitations in the quantum dot increases the Rabi doublet evolves into a more complicated triplet structure.     

Matching energy of unicyclic and bicyclic graphs with a given diameter

Gutman and Wagner proposed the concept of matching energy (ME) and pointed out that the chemical applications of ME go back to the 1970s. Let G be a simple graph of order n and be the roots of its matching polynomial. The ME of G is defined to be the sum of the absolute values of . In this article, we characterize the graphs with minimal ME among all unicyclic and bicyclic graphs with a given diameter d. © 2014 Wiley Periodicals, Inc. Complexity 21: 224–238, 2015