Asymptotic properties of correlation bounds in functional spaces. II

This paper is an extension of [11]. Starting from the results of our first paper we prove by inclusion theorems that bounds for the correlation function of a stationary Gaussian process in the space of continuous functions with weight are strongly consistent and asymptotically normal. We construct the simplest functional confidence intervals in these spaces for the indeterminate correlation function.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 43, No. 3, pp. 322–329, March, 1991.     

Comparison theorems and asymptotic behavior of correlation estimators in spaces of continuous functions. II

This paper is the second part of [12]. Using the comparison theorems which were proved in the first part, the asymptotic normality of the estimator — in a model of a series of several samples — of the correlation function of a stationary Gaussian random process in spaces of continuous functions with weights is established. A method for constructing functional confidence intervals for an unknown correlation function in these spaces is described.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 43, No. 5, pp. 579–583, May, 1991.     

Asymptotic expansions for the distributions of functions of a correlation matrix

This paper deals with asymptotic expansions for the non-null distributions of certain test statistics concerning a correlation matrix in a multivariate normal distribution. For this purpose an asymptotic expansion is given for the distribution of a function of the sample correlation matrix. As special cases of the resulting expansion, asymptotic expansions for the distributions of the sample correlation coefficient, Fisher's z-transformation and arcsine transformation are also given.     

Computation of moment functions for parabolic PDEs with random parameters

This paper deals with different approaches for the computation of stochastic characteristics (such as mean, variance, correlation function, …) of the solution to parabolic PDEs with random parameters, in particular with a random Neumann boundary conditions and a random initial condition. Thereby Finite-Element discretisation of the spatial variables is used for the construction of pathwise solutions. The random influences are assumed to be ε -correlated (cp. [4]) that means the correlation functions vanish if the difference of the arguments exceeds a given correlation length ε . So an asymptotic expansion of higher order with respect to the correlation length for the correlation function of the approximative solution is given. A second possibility is the so called explicit calculation. Examples which compare the different methods can be found in [2]. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A class of stationary random fields with a simple correlation structure

A stationary random field is often more complicated than a univariate stationary time series, since dependence for a random field extends in all directions, while there is only the natural distinction of past and future at any instant in a univariate time series. In this paper we start from a simple correlation structure, derive a class of stationary random fields with the simple correlation function and the simple spectral density function by using linear combinations of separable spatial correlation functions, and discuss a problem of embedding a lattice model into a continuous domain model.     

Modelling Joint Behaviour of Asset Prices Using Stochastic Correlation

Association or interdependence of two stock prices is analyzed, and selection criteria for a suitable model developed in the present paper. The association is generated by stochastic correlation, given by a stochastic differential equation (SDE), creating interdependent Wiener processes. These, in turn, drive the SDEs in the Heston model for stock prices. To choose from possible stochastic correlation models, two goodness-of-fit procedures are proposed based on the copula of Wiener increments. One uses the confidence domain for the centered Kendall function, and the other relies on strong and weak tail dependence. The constant correlation model and two different stochastic correlation models, given by Jacobi and hyperbolic tangent transformation of Ornstein-Uhlenbeck (HtanOU) processes, are compared by analyzing daily close prices for Apple and Microsoft stocks. The constant correlation, i.e., the Gaussian copula model, is unanimously rejected by the methods, but all other two are acceptable at a 95% confidence level. The analysis also reveals that even for Wiener processes, stochastic correlation can create tail dependence, unlike constant correlation, which results in multivariate normal distributions and hence zero tail dependence. Hence models with stochastic correlation are suitable to describe more dangerous situations in terms of correlation risk.

     

Two-point Correlation Function and Feynman-Kac Formula for the Stochastic Heat Equation

In this paper, we obtain an explicit formula for the two-point correlation function for the solutions to the stochastic heat equation on \(\mathbb {R}\). The bounds for p-th moments proved in Chen and Dalang (Ann. Probab. 2015) are simplified. We validate the Feynman-Kac formula for the p-point correlation function of the solutions to this equation with measure-valued initial data.     

Estimating Second-Order Characteristics of Inhomogeneous Spatio-Temporal Point Processes

Non-parametric estimates of the K-function and the pair correlation function play a fundamental role for exploratory and explanatory analysis of spatial and spatio-temporal point patterns. These estimates usually require information from outside of the study region, resulting to the so-called edge effects which have to be corrected. They also depend on first-order characteristics, which have to be estimated in practice. In this paper, we extend classical edge correction methods to the spatio-temporal setting and compare the performance of the related estimators for stationary/non-stationary and/or isotropic/anisotropic point patterns. Further, we explore the influence of the estimated intensity function on these estimators.     

On the Theory of KM2O-Langevin Equations for Stationary Flows (2): Construction Theorem

The aim of the present paper is to construct the KM₂O-Langevin matrix LM([X,Y]) directly from the correlation matrix function R by using (DDT), (FDT) and (PAC) as an algorithm.     

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Homogeneity of variance and correlation coefficients is one of assumptions in the analysis of longitudinal data.However, the assumption can be challenged. In this paper, we mainly propose and analyze nonlinear mixed effects models for longitudinal data with exponential correlation covariance structure, intend to introduce Huber's function in the log likelihood function and get robust estimation (M-estimation) by Fisher scoring method. Score test statistics for homogeneity of variance and correlation coefficient based on M-estimation are then studied. A simulation study is carried to assess the performance of test statistics and the method we proposed in the paper is illustrated by an actual data example.     

Background risk,bivariate risk attitudes,and optimal prevention

This paper extends Eeckhoudt et al.’s (2012) results for precautionary effort to bivariate utility function framework. We establish an equivalence between the agent’s precautionary effort motive and the signs of successive cross-derivatives of the bivariate utility function. We show that the introduction (or deterioration) of an independent background risk induces more prevention to protect against wealth loss provided the individual exhibits correlation aversion of some given order. The conditions on the individual’s risk preferences are given to generate some specific prevention behaviors in the univariate framework with multiplicative risks. Our conclusion also indicates that an increase in the correlation between wealth risk and background risk leads to a reduction in optimal prevention.     

Asymptotic expression for the correlation function of twisted fields in the two-dimensional Dirac model on a lattice

A determinant representation is obtained for the correlation function of twisted fields in the two-dimensional Dirac model on a lattice. These fields are determined by twisted boundary conditions for the Dirac fermions. The asymptotic expression is calculated for the correlation function at large distances (the vacuum expectation of the twisted field) at the critical point and in the scaling region. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 121, No. 2 pp. 329–346, Nember, 1999.     

Structural damage detection strategy using correlation functions under inconsistent excitation

Structural damage detection using vibration response signals is appealing in recent years since it does not require the identification of the modal parameters or building the structures' finite element model, among which the correlation-function-based damage detection methodologies is a novel topic [1]. Beginning with the introduction of the correlation function theory, this paper proposes a new damage detection strategy using the auto correlation function values of vibration response signals of the structure. The maximum value of the auto correlation functions of the vibration responses from different measurement points are used to form the damage index to locate the damage. Differences of the damage index are used to make the damage location more clearly. As in real world applications, structures may undergo different external excitations [2]. Different external excitations are input into the intact and damaged structure. The results from numerical simulation of stiffness reduction detection of a 12-story frame structure show that the proposed strategy can locate the damage correctly and has a very good anti-noise ability under inconsistent external excitations. As only the vibration responses before and after damage are used in this damage detection strategy, it can be a useful tool for structural health monitoring. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Degree of deformation and strength of compact bone tissue during torsion

This paper discusses the variation in the deformation and strength properties of compact bone tissue during torsion in various zones of the cross section of human tibia. A correlation has been found between the specific energy of deformation consumed during the loading process and the level of stress attained. The degree of correlation between the deformation and strength properties of the bone tissue has been studied as a function of the concentration of certain biochemical substances in its composition.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No.5, pp. 911–918, September–October, 1973.     

天然气期货和现货价格间的相关性研究

基于天然气期货价格与现货价格序列间具有强非线性特征,本文将GARCH模型和Copula函数思想进行结合,同时考虑了天然气期货和现货价格间的时变相关结构,构建了时变Copula(GARCH-Normal、GARCH-GED和GARCH-t)模型,利用美国纽约商品交易所(NYMEX)Henry Hub交易中心天然气期货价格和现货价格数据进行实证研究。实证结果表明:GARCH-GED模型能够准确地拟合天然气期货与现货价格时间序列;时变SJC-Copula函数能够更好的描述天然气期货价格与现货价格间的相关性;天然气期货与现货价格间的相关性不是对称的,上尾的相关性小于下尾相的相关性。     

Unification of the kinetic and hydrodynamic approaches in the theory of dense gases and liquids

The paper discusses one of the approaches to the kinetics and hydrodynamics of dense gases and liquids based on modification of Bogolyubov's conditions of correlation weakening for the Liouville equation for the nonequilibrium distribution function. An entropy of a nonequilibrium state that depends on both the kinetic and the hydrodynamic parameters is defined. Generalized transport equations are obtained for the hydrodynamic variables, and these equations are consistent with the kinetic equation for the single-particle distribution function.deceasedV. A. Steklov Mathematics Institute; Moscow Institute of Radio Technology, Electronics, and Automation; Institute of the Physics of Condensed Systems, Ukrainian Academy of Sciences. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 96, No. 3, pp. 325–350, September, 1993.     

Predictive Inference for the Elliptical Linear Model

This paper derives the prediction distribution of future responses from the linear model with errors having an elliptical distribution with known covariance parameters. For unknown covariance parameters, the marginal likelihood function of the parameters has been obtained and the prediction distribution has been modified by replacing the covariance parameters by their estimates obtained from the marginal likelihood function. It is observed that the prediction distribution with elliptical error has a multivariate Student'st-distribution with appropriate degrees of freedom. The results for some special cases such as the Intra-class correlation model, AR(1), MA(1), and ARMA(1,1) models have been obtained from the general results. As an application, theβ-expectation tolerance region has been constructed. An example has been added.     

寡头垄断市场下纯捆绑与部件销售模式的选择模型

本文研究了在寡头市场下部件销售模式和纯捆绑模式的选择问题,分别构建了部件销售模式下和纯捆绑模式下的利润函数,并且在此基础上构建了目标函数。文章突破了传统的生产者主导捆绑策略的模式,而是从全新的视角即消费者和生产者的双重视角研究。研究发现:销售模式的选择依赖于商品预期价格的标准差、商品之间的相关系数、商品之间的需求水平、市场信息的透明程度、消费者的消费经验以及商品之间的兼容程度。     

Maxima and minima of independent and non-identically distributed bivariate Gaussian triangular arrays

In this paper, joint limit distributions of maxima and minima on independent and non-identically distributed bivariate Gaussian triangular arrays is derived as the correlation coefficient of ith vector of given nth row is the function of i/n. Furthermore, second-order expansions of joint distributions of maxima and minima are established if the correlation function satisfies some regular conditions.