On null sequences for Banach operator ideals,trace duality and approximation properties

Let be a Banach operator ideal and X be a Banach space. We undertake the study of the vector space of ‐null sequences of Carl and Stephani on X , , from a unified point of view after we introduce a norm which makes it a Banach space. To give accurate results we consider local versions of the different types of accessibility of Banach operator ideals. We show that in the most common situations, when is right‐accessible for , behaves much alike . When this is the case we give a geometric tensor product representation of . On the other hand, we show an example where the representation fails. Also, via a trace duality formula, we characterize the dual space of . We apply our results to study some problems related with the ‐approximation property giving a trace condition which is used to solve the remaining case () of a problem posed by Kim (2015). Namely, we prove that if a dual space has the ‐approximation property then the space has the ‐approximation property.     

Representation of discrete sequences with high-dimensional iterated function systems

Iterated Function System (IFS) models have been used to represent discrete sequences where the attractor of the IFS is self-affine or piece-wise self-affine in R ² or R ³ (R is the set of real numbers). In this paper, the piece-wise hidden-variable fractal model is extended from R ³ to R ⁿ (n is an integer greater than 3), which is called the high-dimensional piece-wise hidden-variable fractal model. This new model uses a “mapping partial derivative” and a constrained inverse algorithm to identify the model parameters. The model values depend continuously on all the hidden variables. Therefore, the result is very general.     

Genocchi polynomials associated with the Umbral algebra

The aim of this paper is to study on the Genocchi polynomials of higher order on P, the algebra of polynomials in the single variable x over the field C of characteristic zero and P^∗, the vector spaces of all linear functional on P. By using the action of a linear functional L on a polynomial p(x) Sheffer sequences and Appell sequences, we obtain some fundamental properties of the Genocchi polynomials. Furthermore, we give relations between, the first and second kind Stirling numbers, Euler polynomials of higher order and Genocchi polynomials of higher order.     

Sensitivity of risk measures with respect to the normal approximation of total claim distributions

A simple and commonly used method to approximate the total claim distribution of a (possibly weakly dependent) insurance collective is the normal approximation. In this article, we investigate the error made when the normal approximation is plugged in a fairly general distribution-invariant risk measure. We focus on the rate of convergence of the error relative to the number of clients, we specify the relative error’s asymptotic distribution, and we illustrate our results by means of a numerical example. Regarding the risk measure, we take into account distortion risk measures as well as distribution-invariant coherent risk measures.     

半参数回归模型小波估计的弱收敛速度

本文研究了误差为鞅差序列情形下的半参数回归模型.利用小波方法,在相当一般的条件下,得到了参数、非参数估计量的弱收敛速度.     

关于有限群表示范畴上几乎可裂序列的注记(英文)

本文给出几乎可裂序列的Green对应.主要结果为:设X是不可分解非投射kG-模,Y是相应的不可分解非投射kL-模,那么(i)0→Ω~2(X)→(XU)_0→X→0是可裂正和列当且仅当0→Ω~2(Y)→(YU)_0→Y→0是可裂正和列;(ⅱ)0→Ω~2(X)→(X(U)_0→X→0是几乎可裂正和列当且仅当0→Ω~2(Y)→(YU)_0→Y→0是几乎可裂正和列.     

NA样本下线性模型估计矩相合性

在NA样本下讨论了线性回归模型最小二乘估计的r阶矩相合性,并在02时推广了相关文献之结论.     

两两NQD列大数定律的一个注记

利用两两NQD列三级数定理的思想和Chebyshev不等式,研究了两两NQD列在一类广泛条件下的弱大数定律和一类加强条件下的强大数定律,得到了与独立情形一致的结果,还特别讨论了同分布情形,推广了相关文献的结果．