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	1. Reinterpret the concept of measurement uncertainty
	Ye Xiaoming
	Mathematics 19 July 2018
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	Abstract:The existing definition of uncertainty actually violates a basic mathematical concept: the variance of a constant with a definite value is 0. Therefore, various interpretations of uncertainty concept are actually specious. From the perspective of probability theory, this paper will point out the key trouble of existing concept, and fully prove that the uncertainty is actually the evaluation value of probability interval of an error and expresses the possible degree that the measured quantity value is close to the true value, instead of the dispersion of measured quantity value. This will lead to a comprehensive change in the interpretation method of measurement theory.
	TO cite this article:Ye Xiaoming. Reinterpret the concept of measurement uncertainty[OL].[19 July 2018] http://en.paper.edu.cn/en_releasepaper/content/4745739


	2. Interpretations of measurement error theory based on new concepts
	Ye Xiaoming
	Mathematics 04 November 2017
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	Abstract:In several previously published papers, the author proposed a new thinking of measurement theory based on error non-classification philosophy. Based on the new concepts, this paper re-interprets the basic principle of measurement error theory completely from the perspective of mathematics, re-proves the concept logic of error classification and the dispersion concept of uncertainty in existing measurement theory are actually incorrect, and gives a new interpretation method for error evaluation principle and measurement uncertainty concept. Its core ideas are, standard deviation is the evaluation of the probable range of an error instead of the dispersion of a measurement result, and any error has a standard deviation to evaluate its probable range.
	TO cite this article:Ye Xiaoming. Interpretations of measurement error theory based on new concepts[OL].[ 4 November 2017] http://en.paper.edu.cn/en_releasepaper/content/4741855

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	3. Existence of solution to a class of stochastic Riccati equations with constraint
	HAN Yue-cai, Xu Jie
	Mathematics 12 June 2016
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	Abstract: In this paper, the authors investigate a class of stochastic Riccati equation with constraint. Stochastic Riccati equation is a matrix-valued, highly nonlinear backward stochastic differential equation together with an algebraic, matrix positive definiteness constraint. Because of its complex structure, and the equation is matrix-valued, the solvability of the stochastic Riccati equation is very difficult, but is the key to solve the stochastic linear quadratic optimal control problem. The main idea is to replace the stochastic Riccati equation by a backward stochastic differential equation (without including algebraic constraint), and the existence of solution for backward stochastic differential equation enforces the algebraic constraint to be satisfied automatically.
	TO cite this article:HAN Yue-cai, Xu Jie. Existence of solution to a class of stochastic Riccati equations with constraint[OL].[12 June 2016] http://en.paper.edu.cn/en_releasepaper/content/4697832


	4. The Solvability of Forward-Backward Doubly Stochastic Hamiltonian Systems
	HAN Yue-cai, Xu Jie
	Mathematics 07 June 2016
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	Abstract: In this note, we investigate the solvability of a forward-backward doubly stochastic Hamiltonian system withboundary value condition. We show the relationship between a linear forward-backward doubly stochastic Hamiltonian system and a deterministicmatrix-valued Riccati equation. These results help us to investigate fruitful properties of solutions of forward-backward doubly stochastic Hamiltonian with boundary valuecondition.
	TO cite this article:HAN Yue-cai, Xu Jie. The Solvability of Forward-Backward Doubly Stochastic Hamiltonian Systems[OL].[ 7 June 2016] http://en.paper.edu.cn/en_releasepaper/content/4697249


	5. Simulation of two-phase shear flows with the one dimensional turbulence model
	Wu Yuxin,Philip J. Smith,Alan R. Kerstein,Lv Junfu
	Mathematics 28 February 2014
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	Abstract:The One Dimensional Turbulence (ODT) method is used to study spatially developing particle laden shear flows based on a novel proposed particle-eddy interaction model. The instantaneous and average flow fields of the gas phase are simulated with ODT model. The particle motions are tracked with a Lagrangian scheme. When a particle enters an eddy that is given by the ODT simulation, an instantaneous particle-eddy interaction model is used to represent turbulence-induced particle dispersion. The model is validated by comparisons between numerical results and measured data of a two-phase shear flow. Particle-size dependence of particle dispersion is studied. Although turbulent mixing process strengthens the particle dispersion in shear layers, those intermediate particles whose Stokes number are close to unity tend to concentrate in a regular pattern.
	TO cite this article:Wu Yuxin,Philip J. Smith,Alan R. Kerstein, et al. Simulation of two-phase shear flows with the one dimensional turbulence model[OL].[28 February 2014] http://en.paper.edu.cn/en_releasepaper/content/4587931


	6. Optimal reinsurance under M-V criterion for the merger of two company
	XU Wei,GUO Junyi,BAI Lihua
	Mathematics 06 February 2013
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	Abstract:In this paper, the two companies take on the same risk, and the two claim number processes are independent Poisson processes. The optimal criterion is M-V criterion. The problem is converted into solving maximizing the expected utility function, and we get the closed-form expressions.
	TO cite this article:XU Wei,GUO Junyi,BAI Lihua. Optimal reinsurance under M-V criterion for the merger of two company[OL].[ 6 February 2013] http://en.paper.edu.cn/en_releasepaper/content/4520714


	7. A Stochastic Inequality on the Largest Order Statisticsfrom Heterogeneous Gamma Variables
	ZHAO Peng
	Mathematics 17 January 2013
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	Abstract:In this paper, we compare the largest orders statistics arising fromindependent heterogeneous gamma random variables according to thethe reversed hazard rate order. The resultderived here strengthens and generalizes some of the results known inthe literature. Some numerical examples are also provided toillustrate the main result.
	TO cite this article:ZHAO Peng. A Stochastic Inequality on the Largest Order Statisticsfrom Heterogeneous Gamma Variables[OL].[17 January 2013] http://en.paper.edu.cn/en_releasepaper/content/4515984


	8. Moderate deviations for estimators of financial risk under an asymmetric Laplace law
	CAI Yujie,GAO Fuqing,WANG Shaochen
	Mathematics 12 March 2012
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	Abstract:We study moderate deviations of estimators of financial risk under an asymmetric Laplace law. The moderate deviation principles of three kinds of estimators based on parametric and non-parametric methods of VaR and CVaR are obtained by the approximation method and the delta method in large deviations. We also present some numerical comparisons of the estimators.
	TO cite this article:CAI Yujie,GAO Fuqing,WANG Shaochen. Moderate deviations for estimators of financial risk under an asymmetric Laplace law[OL].[12 March 2012] http://en.paper.edu.cn/en_releasepaper/content/4470949


	9. Markov skeleton process in PERT networks
	Xiangxing Kong,Xuan Zhang,Zhenting Hou
	Mathematics 13 January 2009
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	Abstract:In this paper we investigate Programming Evaluation and Review Technique networks with independently and generally distributed activity durations. For any path in this network, we select all the activities related to this path such that the completion time of the sub-network (only consist of all the related activities) is equal to the completion time of this path. We use the elapsed times as the supplementary variables and model this sub-network as a Markov Skeleton Process, the state space is related to the sub-network structure. Then use the backward equation to compute the distribution of the sub-network\
	TO cite this article:Xiangxing Kong,Xuan Zhang,Zhenting Hou. Markov skeleton process in PERT networks [OL].[13 January 2009] http://en.paper.edu.cn/en_releasepaper/content/27699


	10. Multidimensional g-expectations and Risk Measures
	xu yuhong
	Mathematics 02 October 2008
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	Abstract:This paper proposes a notion of multidimensional g-expectations which provide a multidimensional version of nonlinear expectations. By a technical result on explicit expressions for the comparison theorem of multidimensional backward stochastic differential equations, necessary and sufficient conditions are given for the constancy, monotonicity and positivity properties of multidimensional g-expectations; we also prove that a multidimensional risk measure introduced by multidimensional g-expectation is concave if and only if the generator g satisfies a concave-like condition.
	TO cite this article:xu yuhong. Multidimensional g-expectations and Risk Measures[OL].[ 2 October 2008] http://en.paper.edu.cn/en_releasepaper/content/24507

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