关于双重时序AR-MA模型的相关结构及与ARMA模型的比较

本文在文［４］的基础上讨论了双重时序ＡＲ（１）－ＭＡ（ｑ）模型的相关结构，在不假定白噪声序列为正态的情况下，证明了安鸿志［２］关于模型的相关结构的猜想是正确的，具体地构造了ＡＲ（１）－ＭＡ（３）模型的相关结构，并与ＡＲＭＡ模型进行了初步的比较，给出了一些抛砖引玉的讨论．     

4-Aminophthalimide Derivatives as Environment-Sensitive Probes

The potential of 4-aminophthalimide (AP) and its derivatives as fluorescence probes for organized media is highlighted. The fluorescence response of AP, as measured from the position of the fluorescence maximum, fluorescence intensity and lifetime, is highly sensitive to the polarity of the medium. The sensitivity of the fluorescence parameters is further enhanced due to the involvement of the emitting intramolecular charge transfer state in hydrogen bonding interaction with the solvent molecules containing hydroxyl groups. It is shown that the microheterogeneous environments of organized media such as cyclodextrins and micelles can be very conveniently monitored using this probe. The results of the investigations carried out employing AP and its derivatives as fluorescence probe molecules in these media clearly suggest that a combination of the hydrophobic interaction with the host media and hydrogen bonding interaction with the solvent molecules determine the location of the fluorophore, which in all cases is found to be the interfacial region separating the nonpolar core of the micelle or the cyclodextrin cavity and the polar aqueous environment. Guidelines for the design of probes of this class of systems for the nonpolar core region of the micelles are provided and possible ways to increase the sensitivity of the fluorescence response of the systems are suggested.     

“String” formulation of the dynamics of the forward interest rate curve

We propose a formulation of the term structure of interest rates in which the forward curve is seen as the deformation of a string. We derive the general condition that the partial differential equations governing the motion of such string must obey in order to account for the condition of absence of arbitrage opportunities. This condition takes a form similar to a fluctuation-dissipation theorem, albeit on the same quantity (the forward rate), linking the bias to the covariance of variation fluctuations. We provide the general structure of the models that obey this constraint in the framework of stochastic partial (possibly non-linear) differential equations. We derive the general solution for the pricing and hedging of interest rate derivatives within this framework, albeit for the linear case (we also provide in the appendix a simple and intuitive derivation of the standard European option problem). We also show how the “string” formulation simplifies into a standard N-factor model under a Galerkin approximation. Received: 30 January 1998 / Revised: 12 February 1998 / Accepted: 16 February 1998     

Fluctuation kinetics of diffusion-controlled processes: Strong effects due to correlations and fluctuations

We summarize some recent results related to fluctuation-induced kinetics of diffusion-controlled processes. We show that kinetic behavior can be drastically changed due to fluctuation effects, spatial correlations between particles, and anomalous transport properties. In addition, we show that correlation-induced kinetics in some systems can govern the temporal evolution over the entire time domain.     

Modified Equations for Stochastic Differential Equations

We describe a backward error analysis for stochastic differential equations with respect to weak convergence. Modified equations are provided for forward and backward Euler approximations to Itô SDEs with additive noise, and extensions to other types of equation and approximation are discussed.     

随机参数Duffing系统中的随机混沌及其延迟反馈控制

研究了谐和激励下含有界随机参数Duffing系统(简称随机Duffing系统)中的随机混沌及其延迟反馈控制问题.借助Gegenbauer多项式逼近理论，将随机Duffing系统转化为与其等效的确定性非线性系统.这样，随机Duffing系统在谐和激励下的混沌响应及其控制问题就可借等效的确定性非线性系统来研究.分析阐明了随机混沌的主要特点，并采用Wolf算法计算等效确定性非线性系统的最大Lyapunov指数，以判别随机Duffing系统的动力学行为.数值计算表明，恰当选取不同的反馈强度和延迟时间，可分别达到抑制或诱发系统混沌的目的，说明延迟反馈技术对随机混沌控制也是十分有效的. 关键词： 随机Duffing系统 延迟反馈控制 随机混沌 Gegenbauer多项式     

Soluble models for dynamics driven by a super-diffusive noise

We explicitly discuss scalar Langevin type of equations where the deterministic part is linear, but where the integrated noise source is a non-linear diffusion process exhibiting superdiffusive behavior. We calculate transient and stationary probabilities and study the possibility of noise induced transitions from a unimodal to a bimodal probability shape. Illustrations from finance and dynamical systems are given.     

On the Equivalence of Multiparameter Gaussian Processes

Our purpose is to characterize the multiparameter Gaussian processes, that is Gaussian sheets, that are equivalent in law to the Brownian sheet and to the fractional Brownian sheet. We survey multiparameter analogues of the Hitsuda, Girsanov and Shepp representations. As an application, we study a special type of stochastic equation with linear noise.      

Magnetisation reversal in media with perpendicular anisotropy

In this paper, we discuss two key aspects of magnetisation reversal in magnetic thin films with perpendicular anisotropy. Firstly, a study has been made of the additional field required to erase data written perpendicular to a thin film recording disk as the linear data density is increased. It has been found that an increase in data density from 40 to 360 kfci results in an increase of 1.25 kOe in the field required to erase the data. Secondly, the effect of varying the level of exchange coupling by co-sputtering CoCrPt samples with SiO₂ has been studied using a characterisation technique that is independent of the self-demagnetising field. It has been found that the samples are fully exchange de-coupled when the film contains >9.8% SiO₂ and the activation volume of reversal remains constant for higher levels of SiO₂.