Multi-dimensional smoothing transformations: Existence,regularity and stability of fixed points

We analyze a class of smoothing transformations on probability measures in multiple space dimensions. Applying a synthesis of probabilistic methods and Fourier analysis, we prove existence and uniqueness of a fixed point inside the class of probability measures of finite second moment, characterize it as a scale mixture of Gaussians, and discuss its regularity. We also classify its tail, which might be of Pareto type. As an application, we study the stability of stationary solutions in a Kac-type kinetic model. In particular, we prove that the domain of attraction is precisely the probability measures of finite second moment.     

On the application of mixture model for two-phase flow induced corrosion in a complex pipeline configuration

This study introduces the application for the mixture model to simulate the liquid–liquid flow through complex pipeline configurations. The model is validated by comparing model predictions with published experimental data and showed reasonable agreement. The model is used to calculate the naphtha–water flow through a complex pipeline configuration with straight pipes and elbow fittings. The selected pipeline suffers from corrosion problems. The effect of different fittings on the pipeline is taken into account. The results obtained here showed that the mixture model is appropriate two-phase flow model and could be used to explain the reasons why specific locations in the pipeline suffer from corrosion problems while other locations do not suffer from these problems. These locations are predicted with good agreement with field measurements of corrosion distribution. It was concluded through this study that the mixture model can predict the two-phase flow features with reasonable accuracy and during relatively short computational time.     

A Sequential Algorithm for Fast Fitting of Dirichlet Process Mixture Models

In this article, we propose an improvement on the sequential updating and greedy search (SUGS) algorithm for fast fitting of Dirichlet process mixture models. The SUGS algorithm provides a means for very fast approximate Bayesian inference for mixture data which is particularly of use when datasets are so large that many standard Markov chain Monte Carlo (MCMC) algorithms cannot be applied efficiently, or take a prohibitively long time to converge. In particular, these ideas are used to initially interrogate the data, and to refine models such that one can potentially apply exact data analysis later on. SUGS relies upon sequentially allocating data to clusters and proceeding with an update of the posterior on the subsequent allocations and parameters which assumes this allocation is correct. Our modification softens this approach, by providing a probability distribution over allocations, with a similar computational cost; this approach has an interpretation as a variational Bayes procedure and hence we term it variational SUGS (VSUGS). It is shown in simulated examples that VSUGS can outperform, in terms of density estimation and classification, a version of the SUGS algorithm in many scenarios. In addition, we present a data analysis for flow cytometry data, and SNP data via a three-class Dirichlet process mixture model, illustrating the apparent improvement over the original SUGS algorithm.     

Option pricing under a normal mixture distribution derived from the Markov tree model

We examine a Markov tree (MT) model for option pricing in which the dynamics of the underlying asset are modeled by a non-IID process. We show that the discrete probability mass function of log returns generated by the tree is closely approximated by a continuous mixture of two normal distributions. Using this normal mixture distribution and risk-neutral pricing, we derive a closed-form expression for European call option prices. We also suggest a regression tree-based method for estimating three volatility parameters σ, σ⁺, and σ⁻ required to apply the MT model. We apply the MT model to price call options on 89 non-dividend paying stocks from the S&P 500 index. For each stock symbol on a given day, we use the same parameters to price options across all strikes and expires. Comparing against the Black–Scholes model, we find that the MT model’s prices are closer to market prices.     

流体混合物热力学性质计算的混合法则新进展

回顾近期关于流体混合物热物性混合法则的研究新进展,特别是余吉布斯自由能(GE)和余亥姆霍兹自由能(AE)型混合法则的拓展及应用,重点介绍一种基于AE,仅通过偏微分方程便可计算混合物所有热力学性质的混合法则。可为发展未知流体混合物热物性计算方法以及各种常见混合物热物性的工程应用提供参考和依据。     

Pricing perpetual American catastrophe put options: A penalty function approach

The expected discounted penalty function proposed in the seminal paper by Gerber and Shiu [Gerber, H.U., Shiu, E.S.W., 1998. On the time value of ruin. North Amer. Actuarial J. 2 (1), 48-78] has been widely used to analyze the joint distribution of the time of ruin, the surplus immediately before ruin and the deficit at ruin, and the related quantities in ruin theory. However, few of its applications can be found beyond except that Gerber and Landry [Gerber, H.U., Landry, B., 1998. On the discount penalty at ruin in a jump-diffusion and the perpetual put option. Insurance: Math. Econ. 22, 263-276] explored its use for the pricing of perpetual American put options. In this paper, we further explore the use of the expected discounted penalty function and mathematical tools developed for the function to evaluate perpetual American catastrophe equity put options. We obtain the analytical expression for the price of perpetual American catastrophe equity put options and conduct a numerical implementation for a wide range of parameter values. We show that the use of the expected discounted penalty function enables us to evaluate the perpetual American catastrophe equity put option with minimal numerical work.     

聚甲基丙烯酸甲酯与苯乙烯-丙烯腈共聚物混合体系相分离初期的固体NMR研究

本文用氢谱宽线固体NMR技术研究了聚甲基丙烯酸甲酯(PMMA)和苯乙烯-丙烯腈共聚物(SAN)混合体系不稳相分离初期阶段, 得到了在分相过程中弛豫谱的变化规律, 测定了相分离增长速率。结果指出: 随着退火时间的增加, 两相体系形成; 大分子扩散方式是由浓度低的区域向浓度高的区域扩散, 扩散系数为负值; 相分离增长速率的数量级与用光散射研究的结果相同; 分子相互作用的相关距离为46.5 nm。     

非线性混合模式的语音盲分离算法

本文针对FIR非线性混合模型，基于最大熵算法，提出了一种以高斯混合模式概率密度函数估计替代传统对数化概率密度估计的盲分离算法，以偶函数为非线性激活函数，采用最大期望（EM）迭代算法推导了分离算法的权向量迭代公式，通过模拟仿真实验结果与传统的最大熵和高阶累积量方法比较，新算法提高了收敛速度，并有效地完成了非线性语音分离任务，抑制了干扰语音信号的影响，提高了输出信噪比。