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FINDING THE STRICTLY LOCAL AND ε-GLOBAL MINIMIZERS OF CONCAVE MINIMIZATION WITH LINEAR CONSTRAINTS

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Journal of Computational mathematics 1997年第4期15卷 327-334页

作者： Patrice Marcotte (Centre de Recherche sur Les Transports, Universit de Montr al, Queb c, Canada)Shi-quan Wu (probability laboratory,{2., chinese academy of sciences,Beijing, china) Centre de Recherche Sur Les Transports Université de Montréal Que. Canada probability laboratory Institute of Applied Mathematics Chinese Academy of Sciences Beijing China

This paper considers the concave minimization problem with linear constrailits,proposes a technique which may avoid the unsuitable Karush-Kuhn-Tucker poiats,then combines this technique with nank-Wolfe method and simplex method to form a pivoting method which can determine a strictly local minimizer of the problem in a finite number of iterations. Basing on strictly local minimizers, a new cutting plane method is proposed. Under some mild conditions, the new cutting plane method is proved to be finitely terminated at an θ-global minimizer of the problem.

关键词： NLP GLOBAL MINIMIZERS OF CONCAVE MINIMIZATION WITH LINEAR CONSTRAINTS Pro PI FINDING THE STRICTLY LOCAL AND

Uniform estimate for maximum of randomly weighted sums with applications to insurance risk theory

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Science china mathematics 2005年第10期48卷 1379-1394页

作者： WANG Dingcheng~1 SU Chun~2.& ZENG Yong~1 1. School of Management and School of applied mathematics,University of Electronic Science and Technology of{2.,Chengdu 610054,china 2. Department of Statistics and Finance,University of Science and Technology of{2.,Hefei 2.002.,china 1. School of Management and School of applied mathematics University of Electronic Science and Technology of China 610054 Chengdu China 2. Department of Statistics and Finance University of Science and Technology of China 230026 Hefei China

This paper obtains the uniform estimate for maximum of sums of independent and heavy-tailed random variables with nonnegative random weights, which can be arbitrarily dependent of each other. Then the applications to ... 详细信息

关键词： dependent stochastic return, discount factor, heavy-tails, discrete time insurance risk model, maxima of randomly weighted sums, ruin probability, tail probabilities, uniformly asymptotic estimate.

Uniform design over a convex polyhedron

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chinese Science Bulletin 1999年第2期44卷 112-114页

作者： FANG Kaitai , TIAN Guoliang XIE Minyu Hong Kong Baptist University, Kowloon, Hong Kong, china institute of {2. mathematics, chinese academy of sciences, Beijing 100080, china Central china Normal University, Wuhan 430070, chinaCorresponding author: Present address: Department of probability and Statistics, Peking University, Beijing 100871, china Hong Kong Baptist University Hong Kong China institute of applied {2. Chinese Academy of Sciences Beijing China Central china Normal University Wuhan China

A new method, called the simplex method, is proposed to generate the uniform design over a convex polyhedron in n-dimensional Euclidean

关键词： convex polyhedron experimental design uniform design.

Characteristic Rainfall for Warning of Debris Flows

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Journal of Mountain Science 2010年第3期7卷 207-214页

作者： HU Kaiheng Cui Peng Wang Chuanchang Li Yong Lu Xiaobing Key laboratory of Mountain Hazards and Earth Surface Processes Chinese Academy of Sciences Chengdu 610041 China institute of Mountain Hazards and Environment Chinese Academy of Sciences & Ministry of Water Conservancy Chengdu 610041 China institute of Mechanics Chinese Academy of Sciences Beijing 100080 China

A characteristic rainfall is introduced to overcome the difficulties encountered in determining a critical rainfall value for triggering debris *** characteristic value is defined as the rainfall at which debris-flow occurrence probability shows a rapid increase,and can be used as a warning rainfall threshold for debris *** of recorded debris flows and 2.-hour rainfall data at Jiangjia basin,Yunnan Province,in southwestern china,demonstrates the existence of such a characteristic *** was found that the characteristic rainfall corresponds to the daily rainfall of 90% cumulative probability by analyzing the basin's daily rainfall *** result provides a simple and useful method for estimating a debris-flow warning rainfall threshold from the daily rainfall *** was applied to estimate the debris-flow warning rainfall threshold for the Subaohe basin,a watershed in the 2.08 Wenchuan earthquake zone with many physical characteristics similar to those of the Jiangjia basin.

关键词： Debris flow Wenchuan earthquake warning rainfall threshold statistics of daily rainfalldistribution

HEAVY TRAFFIC LIMIT THEOREMS IN FLUID BUFFER MODELS

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Journal of Systems Science & Complexity 2004年第1期17卷 1-15页

作者： YINGang ZHANGHanqin Departmentofmathematics WayneStateUniversityDetroitMI48202USA) instituteofapplied{2. AcademyofMathematicsandSystemsSciencesChineseAcademyofSciencesBeijing100080China

A fluid buffer model with Markov modulated input-output rates is *** traffic intensity is near its critical value, the system is known as in heavy *** is shown that a suitably scaled sequence of the equilibrium buffer contents has a weakor distributional limit under heavy traffic conditions. This weak limit is a functional of adiffusion process determined by the Markov chain modulating the input and output *** first passage time of the reflected process is examined. It is shown that the mean firstpassage time can be obtained via a solution of a Dirichlet problem. Then the transitiondensity of the reflected process is derived by solving the Kolmogorov forward equation witha Neumann boundary condition. Furthermore, when the fast changing part of the generatorof the Markov chain is a constant matrix, the representation of the probability distributionof the reflected process is derived. Upper and lower bounds of the probability distributionare also obtained by means of asymptotic expansions of standard normal distribution.

关键词： fluid model markov chain singular perturbation diffusion process

TAX EVASION:MODELS WITH SELF-AUDIT

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Journal of Systems Science & Complexity 2008年第4期21卷 487-518页

作者： Kin Keung LAI Department of Management sciences City University of Hong Kong College of Business Management Hunan University

Different from traditional tax audit, supervision with self-audit is a combination of audit by the taxpayer himself and audit by the tax authority. This paper mainly studies a taxpayer＇s optimal policy of tax evasion under supervision with self-audit and its related properties, in order to deduce some effective suggestions and theoretical bases to restrain tax evasion. Assuming that only a certain proportion of evaded tax can be discovered when the audit is executed, the authors first formulate a static model with self-audit. This model is divided into two stages. At the first stage, taxpayers declare their taxes, then the tax authority chooses audit objects, based on a known probability, and announces the result; if the taxpayer is chosen, he will enter the second stage, during which he has a chance to pay the evaded tax and the corresponding late fees and then is audited by the tax authority. The authors show the existence and uniqueness of the optimal amount of tax evasion at the first stage and the optimal proportion to self-expose at the second stage. The authors also discuss the related properties of the interior solution, and do elasticity analyses on some parameters. Besides, the authors extend the static model into the corresponding two-period model, and study the existence and uniqueness of the solution of the extended model. Finally, under the assumption that tax evasion can only be discovered with a certain probability when the audit is executed, the authors formulate another static model with self-audit and investigate its properties.

关键词： Existence and uniqueness of the solution self-audit static model tax evasion two-period model.

Some Large Sample Results for a Class of Functionals of Kaplan-Meier Estimator

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Acta Mathematica Sinica,English Series 1998年第2期14卷 191-200页

作者： Wang Qihua (institute of applied {2.,Academia Sinica,Beijing 100080,china) institute of applied {2. Academia Sinica 100080 Beijing China

In this paper,a class of functionals of Kaplan-Meier estimator is *** process martingale methods are used to show the asymptotic normality,and we establish a mean square error inequality and a probability inequality of them without the assumption that F,G are continuous,where F,G are survival time distribution and censoring time distribution respectively.

关键词： Counting Process Martingale Asymptotic normality Mean square error probability inequality

Saddlepoint approximations for studentized compound Poisson sums with no moment conditions in audit sampling

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Science china mathematics 2010年第12期53卷 3131-3138页

作者： ZHOU GuoLiang 1 & ZHOU Wang 2. 1 institute of Accounting and Finance, Shanghai University of Finance and Economics, Shanghai 2.0433, china 2.Department of Statistics and {2. probability, National University of Singapore, Singapore 117546, Singapore 1. institute of Accounting and Finance Shanghai University of Finance and Economics Shanghai 200433 China2. Department of Statistics and Applied Probability National University of Singapore Singapore 117546 Singapore

Saddlepoint approximations for the studentized compound Poisson sums with no moment conditions in audit sampling are derived. This result not only provides a very accurate approximation for studentized compound Poisson sums, but also can be applied much more widely in statistical inference of the error amount in an audit population of accounts to check the validity of financial statements of a firm. Some numerical illustrations and comparison with the normal approximation method are presented.

关键词： saddlepoint approximation Laplace approximation self-normalized compound Poisson sum stu- dentized compound Poisson sum

THE ASYMPTOTICS OF THE INTEGRATEDSQUARE ERROR FOR THE KERNEL HAZARD RATEESTIMATORS WITH LEFT TRENCATED ANDRIGHT CENSORED DATA

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Systems Science and Mathematical sciences 1999年第3期12卷 251-262页

作者： SUN Liuquan(institute of applied {2., Academia Sinica, Beijing 100080, china)ZHENG Zhongguo(Department of probability and Statistics, Peking University, Beijing 100871, china) 中科院应用数学所北京 100080 北京大学概率统计系北京 100871

A central limit theorem for the integrated square error (ISE) of the kernelhazard rate estimators is obtained based on left truncated and right censored data. Anasymptotic representation of the mean integrated square ... 详细信息

关键词： Left truncation and right censorship kernel hazard rate estimators integrated square error central limit theorem an asymptotic representation