证券组合的Markov链模型

本文将证券价格时间序列分解成趋势变动序列和 Markov链 ,建立了证券组合的 Markov链模型 ,应用 Markov链理论对此模型进行了分析 ,给出了充分大的一个时间内的收益率 ,风险和切点组合的计算公式     

非时齐Markov过程的Nash不等式

本文将时齐Markov过程的经典Nash不等式推广到非时齐Markov过程,建立了非时齐Markov过程的转移半群与Nash不等式之间的关系.     

最大祖先图的Markov等价性

研究了最大祖先图(MAnG)的Markov等价性, 得到判断一个MAnG与另一个MAnG,以及与一个有向非循环图Markov等价的充要条件,并且提出了一个把MAnG变换成与其Markov等价的有向非循环图的快速实现算法.     

Markov积分半群的扰动和逼近

为了研究Markov积分半群的扰动和逼近,根据转移函数与Markov积分半群之间一一对应关系,以及转移函数的扰动和逼近,通过积分的方法,获得了Markov积分半群的广义Phillips扰动定理和Trotter-Kato逼近定理.     

改进的带驻留时间隐Markov模型的前向-后向算法

对隐Maxkov模型(hidden Markov model:HMM)的状态驻留时间的概率进行了修订,给出了改进的带驻留时间隐Markov模型的结构,并在传统的隐Markov模型(traditional hidden Markov model:THMM)的基础上讨论了新模型的前向.后向变量,导出了新模型的前向-后向算法的迭代公式,同时也给出了新模型各个参数的重估公式.     

Markov调制L′evy模型定价的Fourier-Cos方法

对一般的Markov调制L′evy模型,利用Fourier Cosine级数展开原理得到欧式期权价格的计算方法。进一步,为了改进期权定价的Fourier Cosine级数展开方法的计算精度, Fourier Cosine级数展开的对象进行了修正,获得了欧式期权价格的修正Fourier Cosine级数展开计算方法。此外,还将获得的方法应用于Markov调制Black-Scholes模型, Markov调制Merton跳扩散模型和Markov调制CGMY L′evy模型期权定价的计算。具体的数值计算说明：修正Fourier Cosine级数展开方法应与Fourier Cosine级数展开方法相比,收敛速度要慢一些,但准确性却有很大的提高。特别是对Markov调制纯跳模型,效果更为显著。     

首达时间:忙期与等待时间

讨论了可数状态Markov过程首达时间的一般表示,研究了Markov过程所对应排队系统的忙期与等待时间的计算问题.特别地,得到了GI/M/1型和M/G/1型Markov过程所对应排队系统忙期与等待时间的简化算法,并给出了数值例子.     

Markov调制Lévy模型定价的Fourier-Cos方法

对一般的Markov调制Lévy模型,利用Fourier Cosine级数展开原理得到欧式期权价格的计算方法.进一步,为了改进期权定价的Fourier Cosine级数展开方法的计算精度,Fourier Cosine级数展开的对象进行了修正,获得了欧式期权价格的修正Fourier Cosine级数展开计算方法.此外,还将获得的方法应用于Markov调制Black-Scholes模型,Markov调制Merton跳扩散模型和Markov调制CGMY Lévy模型期权定价的计算.具体的数值计算说明:修正Fourier Cosine级数展开方法应与Fourier Cosine级数展开方法相比,收敛速度要慢一些,但准确性却有很大的提高.特别是对Markov调制纯跳模型,效果更为显著.     

一类具有非线性发生率和Markov转换的SIS传染病模型

研究一类具有非线性发生率和Markov转换的SIS传染病模型.当Markov链为两个状态时,根据阈值的取值,研究该模型疾病灭绝和持久的性质,其结果可以推广到有限状态空间的Markov链的情形.最后,对主要结论进行了数据拟合.     

Markov 骨架过程的随机时变换

讨论了Markov骨架过程的随机时变换,给出了一类变换Markov骨架过程为Markov骨架过程的随机时变换.     

中国产业结构转移的Markov链

本文提出了系统的结构圆概念 ,引入了结构圆上的 Markov链 ,并且将这一模型应用于我国产业结构转移运动的模拟与研究 .文中完成了产业结构转移概率的估计 ,并且根据估计结果 ,对我国不同时期产业结构的转移运动进行了比较分析     

Slow–fast dynamics of tri-neuron Hopfield neural network with two timescales

The slow-fast dynamics of a tri-neuron Hopfield neural network with two timescales is stated in present paper. On the basis of geometric singular perturbation theory, the transition of the solution trajectory is illuminated, and the existence of the relaxation oscillation with rapid movement process alternating with slow movement process is proved. It is indicated the characteristic of the relaxation oscillation is dependent on the structure of the slow manifold. Moreover, the approximate expression of the relaxation oscillation and its period are obtained analytically. Case studies are given to demonstrate the validity of theoretical results.     

Formation of a transition layer on the fillers of polymer composites

Based on a plane model of composites, the effect of a transition layer on the elastic modulus E_c of the composites is analyzed in the case where, under the action of a load, the transition layer is formed both on the side of matrix and filler. In evaluating E_c, it is assumed that the elastic modulus in the layer grows linearly from the elastic modulus of matrix to that of filler, but pores in the filler are impermeable to matrix macromolecules. Analytic relation ships are found which allow one to determine the volume fractions of the transition layer on the side of matrix and filler if the experimental elastic modulus of the composite is known. These relationships are used to find the magnitude of the layer in epoxy composites with various fillers and to evaluate its effect on the compressive elastic modulus of the composites. __________ Translated from Mekhanika Kompozitnykh Materialov, Vol. 42, No. 5, pp. 693–700, September–October, 2006.     

A Simple Cluster Model for the Liquid–Glass Transition

Using the classical distribution-function approach to simple liquids, we estimate the orientational interaction between clusters consisting of a particle and its nearest neighbors. We show that there are density and temperature ranges where the interaction changes sign as a function of the cluster radius. On this basis, the corresponding model of interacting cubic and icosahedral clusters (of the type of a spin glass model) is proposed and solved in the replica-symmetric approximation. We show that the glass order parameter grows continuously on cooling and the replica-symmetry-breaking temperature can be identified with the glass transition temperature. We also show that on cooling a system of particles with a Lennard-Jones interaction, cubic clusters freeze first. The transition temperature for icosahedral clusters is somewhat lower; therefore, the cubic structure of the short-range order is more likely in a Lennard-Jones glass near transition.     

Mover‐stayer model with covariate effects on stayer's probability and mover's transitions

A discrete time Markov chain assumes that the population is homogeneous, each individual in the population evolves according to the same transition matrix. In contrast, a discrete mover‐stayer (MS) model postulates a simple form of population heterogeneity; in each initial state, there is a proportion of individuals who never leave this state (stayers) and the complementary proportion of individuals who evolve according to a Markov chain (movers). The MS model was extended by specifying the stayer's probability to be a logistic function of an individual's covariates but leaving the same transition matrix for all movers. We further extend the MS model by allowing each mover to have her/his covariates dependent transition matrix. The model for a mover's transition matrix is related to the extant Markov chains mixture model with mixing on the speed of movement of Markov chains. The proposed model is estimated using the expectation‐maximization algorithm and illustrated with a large data set on car loans and the simulation.     

On two-parameter bifurcation analysis of switched system composed of Duffing and van der Pol oscillators

The behaviors of system which alternate between Duffing oscillator and van der Pol oscillator are investigated to explore the influence of the switches on dynamical evolutions of system. Switches related to the state and time are introduced, upon which a typical switched model is established. Poincaré map of the whole switched system is defined by suitable local sections and local maps, and the formal expression of its Jacobian matrix is obtained. The location of the fixed point and associated Floquet multipliers are calculated, based on which two-parameter bifurcation sets of the switched system are obtained, dividing the parameter space into several regions corresponding to different types of attractors. It is found that cascading of period-doubling bifurcations may lead the system to chaos, while fold bifurcations determine the transition between period-3 solution and chaotic movement.     

Constructive and Non-Constructive Infinite Formulas in Computable Structures

A transition from arbitrary -formulas to computable formulas in the class of computable structures is considered. It is shown that transition of a certain type is possible which doubles the complexity of the formulas. In addition, the complexity jump is analyzed for the transition from an arbitrary Scott family consisting of -formulas to a computable Scott family in a fixed computable structure. Exact estimates of this jump are found.     

Direct numerical simulation of transition and turbulence in compressible mixing layer

The three-dimensional compressible Navier-Stokes equations are approximated by a fifth order upwind compact and a sixth order symmetrical compact difference relations combined with three-stage Ronge-Kutta method. The computed results are presented for convective Mach numberMc = 0.8 andRe = 200 with initial data which have equal and opposite oblique waves. From the computed results we can see the variation of coherent structures with time integration and full process of instability, formation of A -vortices, double horseshoe vortices and mushroom structures. The large structures break into small and smaller vortex structures. Finally, the movement of small structure becomes dominant, and flow field turns into turbulence. It is noted that production of small vortex structures is combined with turning of symmetrical structures to unsymmetrical ones. It is shown in the present computation that the flow field turns into turbulence directly from initial instability and there is not vortex pairing in process of transition. It means that for large convective Mach number the transition mechanism for compressible mixing layer differs from that in incompressible mixing layer.     

A reduced domain strategy for local mesh movement application in unstructured grids

Automatic control of mesh movement is mandatory in many fluid flow and fluid-solid interaction problems. This paper presents a new strategy, called reduced domain strategy (RDS), which enhances the efficiency of node connectivity-based mesh movement methods and moves the unstructured grid locally and effectively. The strategy dramatically reduces the grid computations by dividing the unstructured grid into two active and inactive zones. After any local boundary movement, the grid movement is performed only within the active zone. To enhance the efficiency of our strategy, we also develop an automatic mesh partitioning scheme. This scheme benefits from a new quasi-structured mesh data ordering, which determines the boundary of active zone in the original unstructured grid very easily. Indeed, the new partitioning scheme eliminates the need for sequential reordering of the original unstructured grid data in different mesh movement applications. We choose the spring analogy method and apply our new strategy to perform local mesh movements in two boundary movement problems including a multi-element airfoil with moving slat or deforming main body section. We show that the RDS is robust and cost effective. It can be readily employed in different node connectivity-based mesh movement methods. Indeed, the RDS provides a flexible local grid deformation tool for moving grid applications.