Surface measures in infinite-dimensional spaces

We construct surface measures for surfaces of codimensionn≥1 in Banach spaces, and in a wide class of locally convex spaces. It is assumed that the determining function has a continuous derivative along a subspace. Translated fromMatematickeskie Zametki, Vol. 63, No. 1, pp. 106–114, January, 1998. The author wishes to express his gratitude to V. I. Bogachev for suggesting the problem and for his valuable scientific advice.     

Sinai-Ruelle-Bowen Measures for Lattice Dynamical Systems

For weakly coupled expanding maps on the unit circle, Bricmont and Kupiainen showed that the Sinai-Ruelle-Bowen (SRB) measure exists as a Gibbs state. Via thermodynamic formalism, we prove that this SRB measure is indeed the unique equilibrium state for a Hölder continuous potential function on the infinite dimensional phase space. For a more general class of lattice systems that are small perturbations of the uncoupled map lattice, we present the variational principle, the entropy formula, and the formula for the potential function for the SRB measures. For coupled map lattices with nearest neighbor interactions, we give an explicit formula of the potential function for the SRB measure and consequently, obtain the entropy in terms of coupling parameters.     

一类测度值随机过程的大偏差原理

设｛ξλ；λ∈Λ｝是取值于概率空间的随机过程，在一定的条件下，证明｛ξλ；λ∈Λ｝满足大偏差原理．所获结果推广了Ｋｉｆｅｒ的结论．     

关于大经济金融市场

在Aumann大经济框架下，本文给出具有可测空间经纪人的大金融市场模型；讨论了资产结构完全时均衡的存在性；给出了以经纪人代表效用表出形式的金融资产定价公式，它推广[3]中相关内容。模型更贴近于具有对称信息充分竞争的涵义．     

Continuity of convolution semigroups on hypergroups

LetK be a commutative hypergroup with the property that either the identity character is contained in the support of the Plancherel measure onK ^{^}, or the identity character is not isolated inK ^{^} and all characters sufficiently close (but not equal) to the identity character vanish at infinity. We present a shift compactness theorem forK and use this to prove that every symmetric convolution semigroup of probability measures onK is continuous.     

Convergence in measure of logarithmic means of quadratical partial sums of double Walsh-Fourier series

The main aim of this paper is to prove that the logarithmic means of quadratical partial sums of the double Walsh-Fourier series does not improve the convergence in measure. In other words, we prove that for any Orlicz space, which is not a subspace of LlnL(I²), the set of the functions having logarithmic means of quadratical partial sums of the double Walsh-Fourier series convergent in measure is of first Baire category.     

Markov Chain Approximations for Symmetric Jump Processes

Markov chain approximations of reversible jump processes are investigated. Tightness results and a central limit theorem are established. Moreover, given the generator of a reversible jump process with state space ℝ ^d , the approximating Markov chains are constructed explicitly. As a byproduct we obtain a definition of the Sobolev space H ^α/2(ℝ ^d ), α∈(0,2), that is equivalent to the standard one.      

On the approximation of measurable linear functionals

Every Gaussian Radon measure (nonsymmetric) has the Riesz property. On R^∞, a shift μ₀ 1 σ_b of the law μ₀ of the Bernoulli sequence has the Riesz property iff $\text{b ? l}{}^2\text{or}\text{b ?}\text{R}{}_0{}^{\mathrm{\infty }}$.     

Order Properties of the Space of Finitely Additive Transition Functions

The basic order properties, as well as some metric and algebraic properties, are studied of the set of finitely additive transition functions on an arbitrary measurable space, as endowed with the structure of an ordered normed algebra, and some connections are revealed with the classical spaces of linear operators, vector measures, and measurable vector-valued functions. In particular, the question is examined of splitting the space of transition functions into the sum of the subspaces of countably additive and purely finitely additive transition functions.     

Overview of optical techniques that measure displacements: Murray lecture

Optical techniques that measure displacements play a very important role in current experimental mechanics, material sciences and metrology. This paper presents a survey of developments in these techniques from a personal experience point of view. Three main aspects are considered. Mathematical and numerical models used in the interpretation of fringe information and the corresponding data processing techniques. Optical and electro-optical developments that have taken place to improve the sensitivity, and the efficiency of these methods to make them competitive with purely numerical methods. Applications that have arisen from the synergy between advanced computational capabilities and optics are also presented.