Sparre Andersen模型中破产概率的边界

研究在Andersen Spaxre模型中,当破产概率的初始边界已知的时候,根据更新方程和更新方程中函数的单调性来改进破产概率的边界,并进一步改进了严重损失函数G（x,y）的边界．     

Precise rates in the law of the logarithm for the moment convergence in Hilbert spaces

Let （X, Xn; n ≥1） be a sequence of i.i.d, random variables taking values in a real separable Hilbert space （H, ｜｜·｜｜） with covariance operator ∑. Set Sn = X1 ＋ X2 ＋ ... ＋ Xn, n≥ 1. We prove that, for b 〉 -1,
lim ε→0 ε^2（b＋1） ∞ ∑n=1 （logn）^b/n^3/2 E{｜｜Sn｜｜-σε√nlogn}=σ^-2（b＋1）/（2b＋3）（b＋1） B｜｜Y｜^2b＋3
holds if EX=0,and E｜｜X｜｜^2（log｜｜x｜｜）^3bv（b＋4）〈∞ where Y is a Gaussian random variable taking value in a real separable Hilbert space with mean zero and covariance operator ∑, and σ^2 denotes the largest eigenvalue of ∑.     

Instance-optimality in probability with an -minimization decoder

Let Φ(ω), ωΩ, be a family of n×N random matrices whose entries _i,j are independent realizations of a symmetric, real random variable η with expectation and variance . Such matrices are used in compressed sensing to encode a vector by y=Φx. The information y holds about x is extracted by using a decoder . The most prominent decoder is the ℓ₁-minimization decoder Δ which gives for a given the element which has minimal ℓ₁-norm among all with Φz=y. This paper is interested in properties of the random family Φ(ω) which guarantee that the vector will with high probability approximate x in to an accuracy comparable with the best k-term error of approximation in for the range kan/log₂(N/n). This means that for the above range of k, for each signal , the vector satisfies

with high probability on the draw of Φ. Here, Σ_k consists of all vectors with at most k nonzero coordinates. The first result of this type was proved by Wojtaszczyk [P. Wojtaszczyk, Stability and instance optimality for Gaussian measurements in compressed sensing, Found. Comput. Math., in press] who showed this property when η is a normalized Gaussian random variable. We extend this property to more general random variables, including the particular case where η is the Bernoulli random variable which takes the values with equal probability. The proofs of our results use geometric mapping properties of such random matrices some of which were recently obtained in [A. Litvak, A. Pajor, M. Rudelson, N. Tomczak-Jaegermann, Smallest singular value of random matrices and geometry of random polytopes, Adv. Math. 195 (2005) 491–523].     

Bayesian estimation of finite time ruin probabilities

In this paper, we consider Bayesian inference and estimation of finite time ruin probabilities for the Sparre Andersen risk model. The dense family of Coxian distributions is considered for the approximation of both the inter‐claim time and claim size distributions. We illustrate that the Coxian model can be well fitted to real, long‐tailed claims data and that this compares well with the generalized Pareto model. The main advantage of using the Coxian model for inter‐claim times and claim sizes is that it is possible to compute finite time ruin probabilities making use of recent results from queueing theory. In practice, finite time ruin probabilities are much more useful than infinite time ruin probabilities as insurance companies are usually interested in predictions for short periods of future time and not just in the limit. We show how to obtain predictive distributions of these finite time ruin probabilities, which are more informative than simple point estimations and take account of model and parameter uncertainty. We illustrate the procedure with simulated data and the well‐known Danish fire loss data set. Copyright © 2009 John Wiley & Sons, Ltd.     

Numerical characterization of DNA sequences based on the k-step Markov chain transition probability

A DNA sequence can be regarded as a discrete-time Markov chain. Based on k-step transition probabilities, we construct a series of 4 x 4 k-step transition matrices to characterize the DNA primary sequences. According to the properties of Markov chains, we obtain distributions of A, T, C and G, and analyze the changes among them from yesterday to tomorrow. We can calculate the probabilities of nucleotide triples of DNA primary sequences. Finally, we introduce a correlation of this kind of transition matrices and consider it as an invariant to analyze the similarities/dissimilarities of DNA sequences.     

Energy barriers of proton transfer reactions between amino acid side chain analogs and water from ab initio calculations

Proton transfer reactions were studied in all titratable pairs of amino acid side chains where, under physiologically reasonable conditions, one amino acid may function as a donor and the other one as an acceptor. Energy barriers for shifting the proton from donor to acceptor atom were calculated by electronic structure methods at the MP2/6-31++G(d,p) level, and the well-known double-well potentials were characterized. The energy difference between both minima can be expressed by a parabola using as argument the donor-acceptor distance R(DA). In this work, the fit parameters of the quadratic expression are determined for each donor-acceptor pair. Moreover, it was found previously that the energy barriers of the reactions can be expressed by an analytical expression depending on the distance between donor and acceptor and the energy difference between donor and acceptor bound states. The validity of this approach is supported by the extensive new data set. This new parameterization of proton transfer barriers between titratable amino acid side chains allows us to very efficiently estimate proton transfer probabilities in molecular modelling studies or during classical molecular dynamics simulation of biomolecular systems.     

An Energy Interconversion Principle Applied in Reaction dynamics for the determination of equilibrium standard states

Chemical and other reaction theories involving thermodynamical equilibrium states utilize statistical mechanical equilibrium density distributions. Here, a definition of heat-work transformation termed thermo-mechanical coherence is first made, and it is conjectured that most molecular bonds have the above heat-work transformation property, which models a chemical bond as a “centrifugal heat engine”, where the internal energy state need not correspond to any of the standard equilibrium densities. Expressions are derived for the standard Gibbs free energy, enthalpy, and entropy where the bond coordinates need not conform to a non-degenerate Boltzmann state, since bond breakdown and formation are processes that have direction, whereas equilibrium distributions are derived when the Hamiltonian is of fixed form, which is not the case for chemical reactions using localized Hamiltonians. The empirically determined Gibbs free energy from a known molecular dynamics simulation of a dimer reaction , accords rather well with the theoretical estimate. A relation connecting the rate of reaction with the equilibrium constant and other kinetic parameters is derived and could place the commonly observed linear relationship between the logarithms of the rate constant and equilibrium constant on a firmer theoretical footing. These relationships could include analogues of the Hammett correlations used extensively in physical organic chemistry, as well as others which are temperature dependent. One prediction of the principles developed here is that the equilibrium standard reaction free energy is more dependent on the height of the intermolecular potential than its depth, so that the sign of the ΔG ^θ can change for varying barrier height with fixed well depth, which may appear counter-intuitive. All the above developments can be tested directly in simulations and therefore provides a fertile ground for further research with significant implications on how standard states are determined in relation to the direction of chemical reaction.This work treats the molecular bond using standard thermodynamics as if it were a system, and it is anticipated that with the advent of single-molecule science and experiment, that might be one direction in which molecular statistical thermodynamics would develop.     

低频纯音不愉悦感主观评价的实验研究

本文提出分别采用“不愉悦度”和“不愉悦概率”作为衡量低频噪声主观感觉的整体评价指标,并确定出评价等级与相应的计算公式。在此基础上,以人工产生的低频纯音为研究对象,结合“5点4级”评价尺度,采用语义细分法,设计并完成了实验室主观评价实验。分析处理实验数据后发现：（1）“不愉悦度”与“不愉悦概率”两种感觉指标的评价结果之间及其各自所确定的评价等级之间存在较高相关性;（2）A,C及线性声级均可用于衡量低频纯音的不愉悦度,三者的衡量效果基本一致;（3）不同频率低频纯音的不愉悦度随声压级的变化趋势不同。     

混合衰落信道下选择中继译码转发的性能分析

蜂窝中继通信中基站到中继以及中继到移动台可以建模成混合衰落信道,即基站到中继的信道通常经历莱斯衰落,中继到移动台的信道通常经历瑞利衰落。该文研究混合衰落信道下协同通信系统中两跳译码转发方式的性能,首先通过分析推导了基于选择最佳中继的中断概率、误符号率以及误符号率的渐近线的闭式表达式,然后基于误符号率的渐近线给出了一种功率优化方法。蒙特卡洛仿真验证了理论公式,仿真结果显示优化功率分配的性能优于平均功率分配的性能。     

基于贝叶斯信息更新的风险规避库存策略研究

在贝叶斯库存控制研究中一个著名的结论是：当缺货需求不能被观测到时,最优贝叶斯库存水平总会高于短视策略库存水平,原因是决策者需要通过多订货来获取对需求分布的认识. 这是基于风险中性的研究,然后现实中决策者都期望规避风险. 基于贝叶斯信息更新研究了风险规避背景下需求部分可观测的多周期报童问题,决策者的周期内效用函数满足独立可加性公理. 通过引入非正规化概率,研究发现,对风险规避的决策者,当其效用函数具有不变绝对风险规避特征时,最优贝叶斯库存水平也会高于短视策略库存水平. 非正规化概率简化了动态规划方程与结果的证明.