一类P3P问题方程系统的零点分解

在这篇文章 ,我们运用 Wu-Ritt零点分解方法研究了透视 3点 ( P3 P)问题并给出了一类 p3 p问题方程系统的零点分解和求解算法 .     

P2P网络中搭便车行为研究

搭便车现象是P2P网络中普遍存在的问题,当网络中存在大量的搭便车节点时,会导致网络拥塞,降低网络性能,甚至导致整个系统崩溃.对目前主要的搭便车行为进行统计,分析搭便车行为产生的机理以及对网络造成的影响.从信任机制、激励机制、演化博弈和效用4个方面对搭便车行为抑制策略进行研究分析,并通过仿真实验对经典算法进行验证.最后对搭便车行为抑制机制的未来研究方向进行展望.     

无穷维切换机制随机逼近算法的分析

本文分析了一类带切换机制的随机逼近算法.此类随机逼近算法可用于对平稳分布的估计,使用固定步长以跟踪占位测度的增量变化.算法中的切换机制可以由可列无穷维Markov链及双时间尺度刻画.本文得到了跟踪误差的最小二乘估计,并在合理的假设条件下证明了算法的连续时间插值形式弱收敛于一类带切换机制的常微分方程系统.此外,本文也对追踪误差的变化速率进行了分析.     

Markov切换扩散过程的几乎处处渐近稳定性

本文研究一类Markov切换扩散过程的样本轨道长时间行为,分几类情形讨论其几乎处处渐近稳定性.对于Markov链状态空间是有限的这类过程的稳定性,应用Perron-Frobenius定理证明;对于可逆的Markov链且其状态空间是有限的这类过程的稳定性,应用主特征值方法证明;对于Markov链状态空间是可数的这类过程的稳定性,应用有限划分技巧及M-矩阵方法证明.每一种情形,相应的例子给出了说明.进一步,使用得到的理论,对线性Markov切换扩散过程的反馈控制问题进行讨论.     

基于BP神经网络的P2P网贷借款人信用评估

评估借款人信用是P2P网贷公司控制风险的重要步骤,对于网贷公司的正常运行有着极其重要的意义。论文参考商业银行信用指标体系并根据P2P网贷自身特点,建立了P2P网贷借款人的信用评估指标体系。根据建立的指标体系构建相应的BP神经网络模型,并利用一步正切法进行优化。然后选取具有代表性的P2P网贷平台的相关数据,对该模型进行训练和仿真,证明了该模型对P2P网贷平台的风险控制起到一定的作用。     

时滞不确定性Markov切换线性随机微分系统的指数鲁棒稳定性

研究了一类时滞不确定性Markov切换随机微分系统的均方指数鲁棒随机稳定性\bd 系统中的时滞是时变的, 不确定项结构为范数有界, Markov切换是连续时间、离散状态的时齐Markov过程{\bf\!.} 利用随机Lyapunov函数方法和LMI技术, 得到了几个判定系统均方指数鲁棒随机稳定性的充分性条件\bd 一个数值例子说明了判据的有效性和可行性.     

基于Razumikhin-Type理论的中立型随机切换非线性系统的P阶矩稳定性与几乎必然稳定性

研究了中立型随机切换非线性系统的P阶矩稳定性与几乎必然稳定性.采用LyapunovRazumikhin方法和随机分析技术,建立了中立型随机切换非线性系统稳定性的判别准则,给出了中立型随机切换非线性系统稳定的充分条件.最后通过仿真算例表明了所得结果的有效性.     

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考察一类Markov切换时变时滞随机系统的均方指数稳定性. 利用基于Liapunov函数和线性矩阵不等式的方法, 给出了使状态反馈控制系统能克服不确定性和随机干扰, 在均方意义下达到指数稳定的充分条件. 当Markov链遍历所有模态时, 给出了一个独立于Markov链模态集的增益矩阵, 使得状态反馈控制系统均方指数稳定     

带Markov切换的混合随机热传导方程的指数稳定性

研究了带Markov切换和两个独立白噪声的混合随机热传导方程,利用Markov切换理论和热传导方程的性质,求得了方程强解的显示表达式,并给出了强解几乎必然指数稳定的充分条件.最后列举了一些例子阐述Markov切换和白噪声对解稳定性的影响.     

基于改进TOPSIS法的P2P网贷平台运营效率评价北大核心CSCD

近年来,P2P网络借贷发展迅猛,吸引了来自金融、经济、管理等诸多领域研究人员越来越多的关注.如何结合运营数据对P2P网贷平台效率进行综合评价,这对P2P网贷平台的运营管理和投资者的投资决策有着十分重要的影响,目前关于这方面的研究相对欠缺.鉴于此,文章提出数据驱动赋权的改进TOSPSIS法对P2P网贷平台效率进行综合评价.首先,针对TOPSIS法存在的主观权重问题,提出数据驱动赋权的数学模型;其次,利用教与学优化算法确定最优权重,以最大化赋权前后数据的一致性和权重的客观性;最后,结合网贷之家的运营数据应用改进TOPSIS法对100家P2P网贷平台效率进行综合评价.结果表明,基于改进TOPSIS法的评价结果和网贷之家的评价结果具有较高的一致性.     

The Measure-Preserving Shift on the Cantor Set

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Generation of the Exact Distribution and Simulation of Matched Nucleotide Sequences on a Phylogenetic Tree

Nucleotide sequences are often generated by Monte Carlo simulations to address complex evolutionary or analytic questions but the simulations are rarely described in sufficient detail to allow the research to be replicated. Here we briefly review the Markov processes of substitution in a pair of matching (homologous) nucleotide sequences and then extend it to k matching nucleotide sequences. We describe calculation of the joint distribution of nucleotides of two matching sequences. Based on this distribution, we give a method for simulation of the divergence matrix for n sites using the multinomial distribution. This is then extended to the joint distribution for k nucleotide sequences and the corresponding 4 ^k divergence array, generalizing Felsenstein (Journal of Molecular Evolution, 17, 368–376, 1981), who considered stationary, homogeneous and reversible processes on trees. We give a second method to generate matched sequences that begins with a random ancestral sequence and applies a continuous Markov process to each nucleotide site as in Rambaut and Grassly (Computer Applications in the Biosciences, 13, 235–238, 1997); further, we relate this to an equivalent approach based on an embedded Markov chain. Finally, we describe an approximate method that was recently implemented in a program developed by Jermiin et al. (Applied Bioinformatics, 2, 159–163, 2003). The three methods presented here cater for different computational and mathematical limitations and are shown in an example to produce results close to those expected on theoretical grounds. All methods are implemented using functions in the S-plus or R languages.     

Limiting search cost distribution for the move-to-front rule with random request probabilities

Consider a list of n files whose popularities are random. The list is updated according to the move-to-front rule. When the induced Markov chain is at equilibrium, we explicitly compute the limiting distribution of the search-cost per item as n tends to infinity. The uniform distribution results in the largest search cost.     

Syzygies for Metropolis base chains

It is shown that Markov chains for sampling from combinatorial sets in the form of experimental designs can be made more efficient by using syzygies on gradient vectors. Examples are presented.     

Predictors for stationary processes with finite generalized Markovian property

A theorem is proved which establishes the conditions for a Gaussian vector stationary process to be Markovian. For a stationary process with finite generalized Markov property we construct a vector Markov process whose first coordinate coincides with the given process. Applying our theorem to the vector process, we derive formulas for the linear predictor of a process with finite generalized Markov property.Translated from Statisticheskie Metody, pp. 82–90, 1980.I would like to acknowledge the helpful attention of P. N. Sapozhnikov.     

Convergence rates in strong ergodicity for Markov processes

A coupling method is used to obtain the explicit upper and lower bounds for convergence rates in strong ergodicity for Markov processes. For one-dimensional diffusion processes and birth–death processes, these bounds are sharp in the sense that the upper one and the lower one only differ in a constant.     

由环的P-性质所确定的根

定义了环的Ｐ根Ｐ、弱拟Ｐ根Ｐｗ 和拟Ｐ根ＰＱ,证明它们均为Ａｍ ｉｔｓｕｒＫｕｒｏｓｈ 根且Ｐ＝ Ｐｗ 为特殊根,给出了Ｐ半单环的结构定理和Ｐ根的模刻划     

一个关于马尔可夫链的极限定理

给出一个关于可列非齐次马尔可夫链M元状态序组出现频率的新形式的强极限定理,所得结论对任意可列非齐次马尔可夫链普遍成立.     

马氏环境中马氏链的一个概率不等式及其应用

本文研究了马氏环境中马氏链构成的随机变量之和的概率不等式问题.利用了结尾的方法,获得了马氏环境中马氏链构成的随机变量之和的尾部概率不等式,作为结果的应用,给出了将过程限制在(S,S∩F,PS)上的强大数定律.文中提出的方法和结果对研究独立的随机变量之和的大样本性质是十分有用的.     

A χ2 goodness-of-fit test for Markov renewal processesgoodness-of-fit test for Markov renewal processes

A Markov Renewal Process (M.R.P.) is a process similar to a Markov chain, except that the time required to move from one state to another is not fixed, but is a random variable whose distribution may depend on the two states between which the transition is made. For an M.R.P. ofm (<∞) states we derive a goodness-of-fit test for a hypothetical matrix of transition probabilities. This test is similar to the test Bartlett has derived for Markov chains. We calculate the first two moments of the test statistic and modify it to fit the moments of a standard χ². Finally, we illustrate the above procedure numeerically for a particular case of a two-state M.R.P. Dwight B. Brock is mathematical statistican, Office of Statistical Methods, National Center for Health Statistics, Rockville, Maryland. A. M. Kshisagar is Associate Professor, Department of Statistics, Southern Methodist University. This research was partially supported by Office of Naval Research Contract No. N000 14-68-A-0515, and by NIH Training Grant GM-951, both with Southern Methodist University. This article is partially based on Dwight B. Brock's Ph.D. dissertation accepted by Southern Methodist University.