Central Limit Theorems of Local Polynomial Threshold Estimator for Diffusion Processes with Jumps

Central limit theorems play an important role in the study of statistical inference for stochastic processes. However, when the non‐parametric local polynomial threshold estimator, especially local linear case, is employed to estimate the diffusion coefficients of diffusion processes, the adaptive and predictable structure of the estimator conditionally on the σ ‐field generated by diffusion processes is destroyed, so the classical central limit theorem for martingale difference sequences cannot work. In high‐frequency data, we proved the central limit theorems of local polynomial threshold estimators for the volatility function in diffusion processes with jumps by Jacod's stable convergence theorem. We believe that our proof procedure for local polynomial threshold estimators provides a new method in this field, especially in the local linear case.     

Bertrand双寡头对上游供应商行为的演化博弈分析

针对目前普遍存在的供应链上下游由于力量不对等而导致的强势一方向弱势一方转嫁成本的现状,研究力量不对等供应链上零售寡头对上游供应商的行为策略.建立竞争环境下的Bertrand寡头模型,得到双寡头采用不同行为策略的支付矩阵.在此基础上,应用演化博弈论中双种群演化模型进行分析,得到双寡头对上游供应商行为的演化稳定均衡.研究结果表明,由于零售寡头之间的竞争,随着寡头对供应商利益侵占数额的增大,双寡头对上游供应商的均衡策略依次为(转嫁成本,转嫁成本)、(转嫁成本,不转嫁成本)以及(转嫁成本,不转嫁成本)与(不转嫁成本,转嫁成本)共存的情况.同时进一步指出市场容量、寡头实力差距、侵占度等参数变化对演化稳定均衡的影响.     

Detection of changes in a random financial sequence with a stable distribution

Quick detection of unanticipated changes in a financial sequence is a critical problem for practitioners in the finance industry. Based on refined logarithmic moment estimators for the four parameters of a stable distribution, this article presents a stable-distribution-based multi-CUSUM chart that consists of several CUSUM charts and detects changes in the four parameters in an independent and identically distributed random sequence with the stable distribution. Numerical results of the average run lengths show that the multi-CUSUM chart is superior (robust and quick) on the whole to a single CUSUM chart in detecting the shift change of the four parameters. A real example that monitors changes in IBM's stock returns is used to demonstrate the performance of the proposed method.     

Wavelet-based estimation for multivariate stable laws

In this article, an estimation problem for multivariate stable laws using wavelets has been studied. The method of applying wavelets, which has already been done, to estimate parameters in univariate stable laws, has been extended to multivariate stable laws. The proposed estimating method is based on a nonlinear regression model on wavelet coefficients of characteristic functions. In particular, two parametric sub-classes of stable laws are considered: the class of multivariate stable laws with discrete spectral measure, and sub-Gaussian laws. Using a simulation study, the proposed method has been compared with well-known estimation procedures.     

热源为常值的纯辐射换热系统温度场的渐近特性

本文讨论了热源为常值的纯辐射换热系统温度场的渐近特性,对其热平衡方程组结出了稳定性的充分条件,且导出了稳定解。     

具有脉冲扩散的单种群模型的研究

本文讨论了在两个斑块上具有脉冲扩散的单种群模型,证明了在适当条件下系统是一致持久的,并利用单调凸算子理论,得到了系统存在唯一全局渐近稳定的周期解,利用数值模拟进一步证明了所得的结论。     

基于演化博弈的区域高耗能产业退出机制研究

高耗能产业的退出是通过产业结构调整提高区域经济系统能效的基本途径,高耗能产业的退出是一个基于地方政府与相关企业间的演化博弈过程。本文运用演化博弈的基本原理,构建了区域高耗能产业退出机制,着重分析了影响各方博弈主体策略选择的因素,构建了不同策略下参与主体双方的支付函数,并建立相应的复制动态方程,寻求演化稳定策略。     

均衡之法律动力源

源囿于效益与公平失衡的对人的过去行为的未来预期的法律的生成、演进和创新,是经济理性人与道德理性人在一般均衡理论向对策均衡理论转化的推动下,以新型发展观为指导所进行的稳定进化性均衡,从而最终达到权利义务配置的最优状态。     

Products of random variables and star-shaped ordering

It is shown that if V₁ and V₂ are two positive random variables such that V₁ is “star-shaped” with respect to V₂, then for any random variable X with a distribution F(x) such that F(ax) has the monotone likelihood-ratio property, XV₁ is star-shaped with respect to XV₂. This result is then used to prove that the stable laws are star-shaped ordered.     

Threshold-range scaling of excitable cellular automata

Each cell of a two-dimensional lattice is painted one of colors, arranged in a color wheel. The colors advance (k tok+1 mod ) either automatically or by contact with at least a threshold number of successor colors in a prescribed local neighborhood. Discrete-time parallel systems of this sort in which color 0 updates by contact and the rest update automatically are called Greenberg-Hastings (GH) rules. A system in which all colors update by contact is called a cyclic cellular automation (CCA). Started from appropriate initial conditions, these models generate periodic traveling waves. Started from random configurations the same rules exhibit complex self-organization, typically characterized by nucleation of locally periodic ram's horns or spirals. Corresponding random processes give rise to a variety of forest fire equilibria that display large-scale stochastic wave fronts. This paper describes a framework, theoretically based, but relying on extensive interactive computer graphics experimentation, for investigation of the complex dynamics shared by excitable media in a broad spectrum of scientific contexts. By focusing on simple mathematical prototypes we hope to obtain a better understanding of the basic organizational principles underlying spatially distributed oscillating systems.