On the estimation of nonlinear time series models

In the present paper, a framework for parametric estimation in nonlinear time series is developed. Strong consistency and asymptotic normality of minimum Hellinger distance estimates for a determined class of nonlinear models are investigated. The main Interest for these estimates is motivated by their robustness under perturbations as it has been emphazized in Beran [2]. The first part of the paper is devoted to the study of some probabilistic properties which ensure the existence and the optimal properties of the estimates     

Invertibility of a linear combination of two matrices and partial orderings

In this paper, we present some results relating different matrix partial orderings and the invertibility of a linear combination of EP matrices.     

Representation of the inverse of a frame multiplier

Certain mathematical objects appear in a lot of scientific disciplines, like physics, signal processing and, naturally, mathematics. In a general setting they can be described as frame multipliers, consisting of analysis, multiplication by a fixed sequence (called the symbol), and synthesis. In this paper we show a surprising result about the inverse of such operators, if any, as well as new results about a core concept of frame theory, dual frames. We show that for semi-normalized symbols, the inverse of any invertible frame multiplier can always be represented as a frame multiplier with the reciprocal symbol and dual frames of the given ones. Furthermore, one of those dual frames is uniquely determined and the other one can be arbitrarily chosen. We investigate sufficient conditions for the special case, when both dual frames can be chosen to be the canonical duals. In connection to the above, we show that the set of dual frames determines a frame uniquely. Furthermore, for a given frame, the union of all coefficients of its dual frames is dense in ?²${?}^2$. We also introduce a class of frames (called pseudo-coherent frames), which includes Gabor frames and coherent frames, and investigate invertible pseudo-coherent frame multipliers, allowing a classification for frame-type operators for these frames. Finally, we give a numerical example for the invertibility of multipliers in the Gabor case.     

Cavitation,Invertibility, and Convergence of Regularized Minimizers in Nonlinear Elasticity

We prove that energy minimizers for nonlinear elasticity in which cavitation is allowed only at a finite number of prescribed flaw points can be obtained, in the limit as ε→0, by introducing micro-voids of radius ε in the domain at the prescribed locations and minimizing the energy without allowing for cavitation. This extends the result by Sivaloganathan, Spector, and Tilakraj (SIAM J. Appl. Math. 66:736–757, 2006) to the case of multiple cavities, and constitutes a first step towards the numerical simulation of cavitation (in the nonradially-symmetric case).      

非线性Lipschitz算子的定量性质(V)──数值值域

本文引入 Ｂａｎａｃｈ空间上非线性 Ｌｉｐｓｃｈｉｔｚ算子 Ｔ的另一个重要定量特性——数值值域Ｗ（Ｔ）．我们证明： Ｗ（Ｔ）与Ｇｅｒｓｃｈｇｏｉｎ域Ｇ（Ｔ）及谱集σ（Ｔ）具有关系σ（Ｔ） ■ ＣｏＷ（Ｔ）＝ Ｇ（Ｔ）．同时,利用此数值域,我们对算子可逆,稳定与压缩的定量性质进行了深入的研究．     

ON THE STATIONARITY AND INVERTIBILITY OF A GENERAL BILINEAR TIME SERIES MODEL

In this paper, some statistical properties of a general bilinear time series model BL (n,m,p,q) are discussed. The sufficient conditions for asymptotic stationarity and invertibility are derived and the expressions of the autocovariance are also given for this model. Results of derivation show that the expressions of autocovariance for a bilinear model are quite different to that of a linear model in the case of q≥ 2 .