Non parametric estimation of the diffusion coefficients of a diffusion with jumps

In this article, we consider a jump diffusion process ${\left(X_t\right)}_{t\ge 0}$, with drift function $b$, diffusion coefficient $\sigma$ and jump coefficient ${\xi }^2$. This process is observed at discrete times $t=0,\Delta ,\dots ,n\Delta$. The sampling interval $\Delta$ tends to 0 and the time interval $n\Delta$ tends to infinity. We assume that ${\left(X_t\right)}_{t\ge 0}$ is ergodic, strictly stationary and exponentially $\beta$-mixing. We use a penalized least-square approach to compute adaptive estimators of the functions ${\sigma }^2+{\xi }^2$ and ${\sigma }^2$. We provide bounds for the risks of the two estimators.     

Wavelet-based estimator for the hurst parameters of fractional brownian sheet

It is proposed a class of statistical estimators H =(H_1,…,H_d) for the Hurst parameters H =(H_1,…,H_d) of fractional Brownian field via multi-dimensional wavelet analysis and least squares,which are asymptotically normal.These estimators can be used to detect self-similarity and long-range dependence in multi-dimensional signals,which is important in texture classification and improvement of diffusion tensor imaging(DTI) of nuclear magnetic resonance(NMR).Some fractional Brownian sheets will be simulated and the simulated data are used to validate these estimators.We find that when H_i ≥ 1/2,the estimators are accurate,and when H_i 1/2,there are some bias.     

Cu Doping-Induced Transformation from [Ag62S12(SBut)32]2+ to [Ag62−xCuxS12(SBut)32]4+ Nanocluster

The change in the valence state of nanocluster can induce remarkable changes in the properties and structure. However, achieving the valence state changes in nanoclusters is still a challenge. In this work, we use Cu²⁺ as dopant to “oxidize” [Ag₆₂S₁₂(SBu^t)₃₂]²⁺ (4 free electrons) to obtain the new nanocluster: [Ag_62−xCu_xS₁₂(SBu^t)₃₂]⁴⁺ with 2 free electrons. As revealed by its structure, the [Ag_62−xCu_xS₁₂(SBu^t)₃₂]⁴⁺ (x=10∼21) has a similar structure to that of [Ag₆₂S₁₂(SBu^t)₃₂]²⁺ precursor and all the Cu atoms occupy the surface site of nanocluster. It′s worth noting that with the Cu atoms doping, the [Ag_62−xCu_xS₁₂(SBu^t)₃₂]⁴⁺ nanocluster is more stable than [Ag₆₂S₁₂(SBu^t)₃₂]²⁺ at higher temperature and in electrochemical cycle. This result has laid a foundation for the subsequent application and exploration. Overall, this work reveals crystals structure of a new Ag−Cu nanocluster and offers a new insight into the electron reduction/oxidation of nanocluster.     

A phenomenological model of electrorheological fluids

The fundamental assumption of the paper is that the extra stress tensor 62xtbvd/xxlarge964.gif" alt="tau" align="BASELINE" BORDER="0"> of an electrorheological fluid is an isotropic tensor valued function of the rate of strain tensor D and the vector n (which characterizes the orientation 62xtbvd/s00397-003-0320-0etIEq1.gif" alt="$${\mathbf{\hat{n}}}$$" align="middle" border="0"> and length N of the fibers formed by application of an electric field). The resulting constitutive equation for 62xtbvd/xxlarge964.gif" alt="tau" align="BASELINE" BORDER="0"> is supplemented by the solution of the previously studied time evolution equation for n. Plastic behavior for the shear and normal stresses is predicted. Anticipating that the action of increasing shear rate 62xtbvd/s00397-003-0320-0etIEq14.gif" alt="$$ \dot{\gamma } $$" align="middle" border="0"> is i) to orient the fibers more and more in the direction of flow and ii) simultaneously to break up the fibers leads to the conclusion that for 62xtbvd/s00397-003-0320-0etIEq15.gif" alt="$$ \dot{\gamma } \to \infty $$" align="middle" border="0"> the same behavior is encountered as without an electric field. Using realistically possible approximation formulas for the dependence of 62xtbvd/s00397-003-0320-0etIEq2.gif" alt="$${\mathbf{\hat{n}}}$$" align="middle" border="0"> and N on 62xtbvd/s00397-003-0320-0etIEq16.gif" alt="$$ \dot{\gamma } $$" align="middle" border="0"> leads to the Bingham behavior for 62xtbvd/s00397-003-0320-0etIEq17.gif" alt="$$ \dot{\gamma } \to 0 $$" align="middle" border="0"> and power law behavior for large shear rates.

A family of minimax rates for density estimators in continuous time

In continuous time, rates of convergence of density estimators fluctuate with the nature of observed sample paths. In this paper, we give a family of rates reached by the kernel estimator and we show that these rates are minimax. Finally, we study applications of these results for specific classes of processes including the Gaussian ones     

Duality methods for a class of quasilinear systems

Duality methods are used to generate explicit solutions to nonlinear Hodge systems, demonstrate the well-posedness of boundary value problems, and reveal, via the Hodge–Bäcklund transformation, underlying symmetries among superficially different forms of the equations.     

Cofinal elementary extensions

We investigate some properties of ordered structures that are related to their having cofinal elementary extensions. Special attention is paid to models of some very weak fragments of Peano Arithmetic.     

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.     

Weak invariance principles for sums of dependent random functions

Motivated by problems in functional data analysis, in this paper we prove the weak convergence of normalized partial sums of dependent random functions exhibiting a Bernoulli shift structure.     

Scaling limits of coupled continuous time random walks and residual order statistics through marked point processes

A continuous time random walk (CTRW) is a random walk in which both spatial changes represented by jumps and waiting times between the jumps are random. The CTRW is coupled if a jump and its preceding or following waiting time are dependent random variables (r.v.), respectively. The aim of this paper is to explain the occurrence of different limit processes for CTRWs with forward- or backward-coupling in Straka and Henry (2011) [37] using marked point processes. We also establish a series representation for the different limits. The methods used also allow us to solve an open problem concerning residual order statistics by LePage (1981) [20].