On the Expectations of Multiple Stratonovich Integrals

Abstract

In the construction of numerical methods for solving stochastic differential equations it becomes necessary to calculate the expectations of products of multiple stochastic integrals. In the Itô case, explicit formulae for the expectation of a multiple integral with integrand identically equal to 1 and for the product of two such integrals are known. In this paper formulae for the expectation of any multiple Stratonovich integral as well as for the product of a broad class of two Stratonovich integrals have been derived.     

模糊随机变量线性规划的求解

研究一种软件算,背景是社会经济规划、工程产业等的计算数据带有主观意识的情形,即往往在目标函数和制约性问题中存在两种不同类型的非确定性;参变量是模糊的和随机的。本文认为可以用可能民生期望原则均混这两类非确定性,从而把模糊随机变量的线性规划问题简化为带有模糊系数的革种标准线性规划问题来求解。     

Expectation formation in an experimental foreign exchange market

Participants of an experimental foreign exchange market forecast an exchange rate with an unknown price reaction function. Aggregate demand is derived from their own forecasts and random shocks. Our experimental results indicate that the expectations of the subjects tend to be coordinated on a common prediction strategy. This strategy is best described as a trend-extrapolative, destabilizing expectation formation scheme. Deviations from common expectations are mainly caused by random shocks, which can be ascribed to the similarity of the subjects’ behavior within and between the different markets. The findings can be explained using insights of behavioral economics.     

评“量子力学中可观察量A在态 ψ中的平均值的定义”(英文)

本文指出用概率方法与用泛函方法定义量子力学中“可观察量在态中的平均值”是有区别的，而唯一正确的方法应为采用概率的方法从而澄清了绝大多数量子力学文献中对于“平均值”概念的某些误解     

基于内部学习动机的中学物理课堂引入

分析了认知学习理论中的学习动机的构成,认为在中学物理课堂引入环节教学,通过创设问题情境,激发学习需要;随之剖析问题情境,帮助学生形成学习期待,可有效地激励出其物理学习动机;然后及时运用所学知识消除问题情境,以求达到进一步强化学习动机的目的.     

Expanded theory for the resolving power of a linear ion mobility spectrometer

An expanded theory for the resolving power of a linear ion mobility spectrometer (IMS) is derived. By definition, the resolving power is directly proportional to the total drift time for the ion through the drift tube divided by the full-width-at-half-height (FWHH) of the observed ion mobility peak. Two approaches to theoretically estimating these two parameters are possible, depending on the operating parameters of the IMS cell. The drift time is given by the first moment of the IMS response. If the electric fields (assumed uniform) are equal in both the shutter/aperture and aperture/collector region, the FWHH is given by a difference in error functions. If the electric fields (again assumed uniform) are not equal, the FWHH is given by the second central moment of the IMS response and can only be known to within a multiplicative factor. The effectiveness of these two approaches is demonstrated using IMS data from the published literature.The additional peak broadening often observed in a linear IMS has several possible sources. One depends on the construction of the cell and the parallelism (or lack thereof) that might exist between the aperture grid and ion collector. Another depends on electric fields used to bias the cell. If the electric field in the aperture/collector region is less than in the shutter/aperture region, peak broadening occurs. Induction effects in the aperture/collector region not only shorten drift times, but also create diffusion-like broadening of the peak. Shortening the distance between the aperture grid and ion collector, or using a higher electric field in that region, minimizes induction effects. Drift time calibration requires adjustments for induction effects.     

The expectation and variance of the joint linear complexity of random periodic multisequences

The linear complexity of sequences is one of the important security measures for stream cipher systems. Recently, in the study of vectorized stream cipher systems, the joint linear complexity of multisequences has been investigated. By using the generalized discrete Fourier transform for multisequences, Meidl and Niederreiter determined the expectation of the joint linear complexity of random N-periodic multisequences explicitly. In this paper, we study the expectation and variance of the joint linear complexity of random periodic multisequences. Several new lower bounds on the expectation of the joint linear complexity of random periodic multisequences are given. These new lower bounds improve on the previously known lower bounds on the expectation of the joint linear complexity of random periodic multisequences. By further developing the method of Meidl and Niederreiter, we derive a general formula and a general upper bound for the variance of the joint linear complexity of random N-periodic multisequences. These results generalize the formula and upper bound of Dai and Yang for the variance of the linear complexity of random periodic sequences. Moreover, we determine the variance of the joint linear complexity of random periodic multisequences with certain periods.     

Dealing with missing values and outliers in principal component analysis

An efficient methodology for dealing with missing values and outlying observations simultaneously in principal component analysis (PCA) is proposed. The concept described in the paper consists of using a robust technique to obtain robust principal components combined with the expectation maximization approach to process data with missing elements. It is shown that the proposed strategy works well for highly contaminated data containing different amounts of missing elements. The authors come to this conclusion on the basis of the results obtained from a simulation study and from analysis of a real environmental data set.     

A systematic comparison of professional exchange rate forecasts with the judgemental forecasts of novices

Professional forecasters in foreign exchange markets are not able to beat naive forecasts. In order to find reasons for this phenomenon we compare the empirical forecasts of experts with the experimentally generated forecasts of novices for the EUR/USD exchange rate in three different forecast horizons. Although the subjects are only provided with the realizations of the exchange rate and are not supported by any statistical procedures they outperform experts in accuracy. Professionals consistently expect a reversal of forgoing exchange rate changes whereas novices extrapolate trends. The judgemental forecasts appear to be unbiased and professionals appear to be biased. We demonstrate that professionals are influenced by the fundamental value—an irrelevant anchor in speculative exchange markets. The poor performance of the experts is not a common failure of human decision-making in market environments but caused by misleading information.     

Heuristic modeling of expectation formation in a complex experimental information environment

Academic subjects made judgmental forecasts of a graphically presented time series in a laboratory experiment. Besides the past realizations of the time series itself, the only available information for the forecasting task was provided by leading series, i.e. indicators with a constant lead period of one. The number and the quality of the leading series were varied systematically between seven versions of the experiment resulting in different levels of information complexity. We present a heuristic that explains the subjects’ average forecasting behavior better than the rational expectations hypothesis in all versions of the experiment. Furthermore, we find that the forecasting accuracy of the subjects increases with the number of reliable indicators but their efficiency declines with increasing complexity.