A Complete Convergence Theorem for Row Sums from Arrays of Rowwise Independent Random Elements in Rademacher Type p Banach Spaces

We extend in several directions a complete convergence theorem for row sums from an array of rowwise independent random variables obtained by Sung, Volodin, and Hu [8 Sung , S.H. , Volodin , A.I. , and Hu , T.-C. ( 2005 ). More on complete convergence for arrays. Statist. Probab. Lett. 71:303–311.  [Google Scholar]] to an array of rowwise independent random elements taking values in a real separable Rademacher type p Banach space. An example is presented which illustrates that our result extends the Sung, Volodin, and Hu result even for the random variable case.     

Distance unimodular equivalence of graphs

Let G be a connected graph and D(G) be its distance matrix. In this article, the Smith normal forms of the integer matrices D(G) are determined for trees, wheels, cycles, complements of cycles and are reduced for complete multipartite graphs.     

Some applications of L2-hedging with a non-negative wealth process

We consider the problem of L ²-hedging of contingent claims in diffusion type models for securities markets. In contrast to a recent paper of Schweizer (1994) we insist on a non-negative wealth process corresponding to the optimal hedge portfolio. For this reason the usual projection methods cannot be applied. We give some applications of L ²-hedging in this setting including hedging under constraints, a problem of approximating the wealth process of a richer investor and a mean-variance version of it.     

Constructing Almost Excellent Unique Factorization Domains

Abstract

Let (T, M) be a complete local normal integral domain containing the rationals such that |T/M | ≥ c where c is the cardinality of the real numbers. Let p be a non-maximal prime ideal of T such that _{T p} is a regular local ring. We construct a local Unique Factorization Domain (UFD) A such that the M-adic completion of A is T, p is maximal in the generic formal fiber and all fibers of A are geometrically regular except for those over some height one prime ideals.

     

关于B值随机和的完全收敛性的进一步讨论

该文在深入揭示B值非随机和完全收敛性中的一系列等价关系的基础上，给出了随机和完全收敛的充分条件，改进和完善了有关文献中的既有成果，并对矩条件的必要性问题做了初步讨论．     

Complete Surjections and Complete Epimorphisms over Completely Distributive Lattices

Generators and lattice properties of the poset of complete homomorphisic images of a completely distributive lattice are exploited via the localic methods. Some intrinsic and extrinsic conditions about this poset to be a completely distributive lattice are given. It is shown that the category of completely distributive lattices is co-well-powered,and complete epimorphisms on completely distributive lattice are not necessary to be surjections. Finally, some conditions about complete epimorphisms to be surjections are given.     

A two-sided estimate in the Hsu-Robbins-Erdös law of large numbers

Let X₁, X₂, … be independent identically distributed random variables. Then, Hsu and Robbins (1947) together with Erdös (1949, 1950) have proved that

,

if and only if E[X²₁] < ∞ and E[X₁] = 0. We prove that there are absolute constants C₁, C₂ (0, ∞) such that if X₁, X₂, … are independent identically distributed mean zero random variables, then

c₁λ⁻² E[X₁²·1_{|X1|λ}]S(λ)C₂λ⁻² E[X₁²·1_{|X1|λ}]

,

for every λ > 0.