NONLINEAR EXPECTATIONS AND NONLINEAR MARKOV CHAINS

§1.IntroductionLet(?,F)be a measurable space and let Lb(F)be the space of F-measurable andbounded real functions.A nonlinear expectation is a continuous functionalE[·]:Lb(F)?→Rthat is order preserving(i.e.,E[X1]≥E[X2],if X1≥X2)and constant preserving     

On the Existence of Positive Solution for n OrderSingular Boundary Value Problems

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On the worst conditional expectation

We study continuous coherent risk measures on L^p, in particular, the worst conditional expectations. We show some representation theorems for them, extending the results of Artzner, Delbaen, Eber, Heath, and Kusuoka.     

一个矩阵不等式和Bayes无偏估计（英）

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A New and Self-Contained Proof of Borwein’s Norm Duality Theorem

Borwein’s norm duality theorem establishes the equality between the outer (inner) norm of a sublinear mapping and the inner (outer) norm of its adjoint mappings. In this note we provide an extended version of this theorem with a new and self-contained proof relying only on the Hahn-Banach theorem. We also give examples showing that the assumptions of the theorem cannot be relaxed. This author is supported by Grant BES-2003-0188 from FPI Program of MEC (Spain).     

连续随机变量的随机独立性与回归独立性

回归独立性是指给定随机变量 X时 ,随机变量 Y的条件期望 E( Y|X)不依赖于 X.前人讨论了离散型随机变量回归独立性与随机独立性的关系 ,得到了二者等价的充分必要条件 .对连续型随机变量的情形加以讨论 ,获到了二者等价的几个充分必要条件 ,并说明在统计分析中的应用 .     

局部紧Vilenkin群上一类次线性算子的加权不等式

本文得到局部紧Vilenkin群上满足一定尺寸条件的一类次线性算子在加幂权Lebesgue空间的强有界和弱有界定理     

ON THE EXPECTATION AND VARIANCE OF HAMMING DISTANCE BETWEEN TWO I.I.D RANDOM VECTORS

1.IntroductionLetFZn={0,1}"beann-dimensionalvectorspaceoverthebinaryfieldFZ={0,1}.TheHammingdistancebetweentwovectorsx=(xl,'tx.)andy=(yi,'ty.)isthenumberofcoordinateswheretheydiffer,andisdenotedbydH(x,y),dH(X,y)=ZIXi~ail.i=1TheHammingweightofxisthenumberofnon-zerocoordinates,andisdenotedbyWH(x).ObviouslyAH(x)=dH(x,0),where0isthezerovector.Thescalarproductofxandyis(x,y)=xlyl ' xestinF2.ForasetAgFZn,IAIdenotesthecardinalityofA.TheaveragedistanceinAisdefinedby*Thisresearchissupp…     

Local reconstruction of low‐rank matrices and subspaces

We study the problem of reconstructing a low‐rank matrix, where the input is an n × m matrix M over a field and the goal is to reconstruct a (near‐optimal) matrix that is low‐rank and close to M under some distance function Δ. Furthermore, the reconstruction must be local, i.e., provides access to any desired entry of by reading only a few entries of the input M (ideally, independent of the matrix dimensions n and m). Our formulation of this problem is inspired by the local reconstruction framework of Saks and Seshadhri (SICOMP, 2010). Our main result is a local reconstruction algorithm for the case where Δ is the normalized Hamming distance (between matrices). Given M that is ‐close to a matrix of rank (together with d and ), this algorithm computes with high probability a rank‐d matrix that is ‐close to M. This is a local algorithm that proceeds in two phases. The preprocessing phase reads only random entries of M, and stores a small data structure. The query phase deterministically outputs a desired entry by reading only the data structure and 2d additional entries of M. We also consider local reconstruction in an easier setting, where the algorithm can read an entire matrix column in a single operation. When Δ is the normalized Hamming distance between vectors, we derive an algorithm that runs in polynomial time by applying our main result for matrix reconstruction. For comparison, when Δ is the truncated Euclidean distance and , we analyze sampling algorithms by using statistical learning tools. A preliminary version of this paper appears appears in ECCC, see: http://eccc.hpi-web.de/report/2015/128/ © 2017 Wiley Periodicals, Inc. Random Struct. Alg., 51, 607–630, 2017     

The valuation of life contingencies: A symmetrical triangular fuzzy approximation

This paper extends the framework for the valuation of life insurance policies and annuities by Andrés-Sánchez and González-Vila (2012, 2014) in two ways. First we allow various uncertain magnitudes to be estimated by means of fuzzy numbers. This applies not only to interest rates but also to the amounts to be paid out by the insurance company. Second, the use of symmetrical triangular fuzzy numbers allows us to obtain expressions for the pricing of life contingencies and their variability that are closely linked to standard financial and actuarial mathematics. Moreover, they are relatively straightforward to compute and understand from a standard actuarial point of view.