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BACKWARD STOCHASTIC VIABILITY AND RELATED PROPERTIES ON Z FOR BSDES WITH APPLICATIONS

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Journal of Systems Science & Complexity 2012年第4期25卷 675-690页

作者： Zhen WU Zhiyong YU School of Mathematics Shandong University School of economics Shandong University

This paper investigates some important properties of Z, the martingale integrant of the backward stochastic differential equations, which is the second process of the solution. These include the backward stochastic viability property, bounded property and the comparison theorem. To explain the theoretical results, the authors apply them to study a financial contingent claim pricing problem. The replication portfolio process can be characterized clearly.

关键词： Backward stochastic differential equations backward stochastic viability property Malliavin calculus portfolio choice.

Research on the threshold effect of population aging on the industrial structure upgrading in China

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Chinese Journal of Population,Resources and Environment 2019年第1期17卷 87-100页

作者： Chengkun Liu Shuyu Li Xindong Zhao School of economics and finanee Huaqiao University Quanzhou China

This paper constructs coefficients of the integral and the internal structure upgrading in the secondary and tertiary industries, selects per capita real gross domestic product as a threshold variable and build panel threshold model according to inter-provincial panel data of China from 1998 to 2016. Results indicated that population aging has a double threshold effect on the integral industrial structure upgrading, whose influence increases first and then decreases, significantly promoting the upgrading process. As for internal structure, population aging has no significant threshold effect on the upgrading in the secondary industry, but exerts a single negative threshold effect in the tertiary industry. When economic development is under the threshold, its negative impact is greater. Further analysis also suggests that regional differences exist significantly in the threshold effect of population aging on the industrial structure upgrading.

关键词： Population aging industrial structure upgrading threshold effect

STOCHASTIC MAXIMUM PRINCIPLE FOR MIXED REGULAR-SINGULAR CONTROL PROBLEMS OF FORWARD-BACKWARD SYSTEMS

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Journal of Systems Science & Complexity 2013年第6期26卷 886-901页

作者： ZHANG Feng School of Mathematics and Quantitative economics Shandong University of Finance and Economics

This paper considers a stochastic optimal control problem of a forward-backward system with regular-singular controls where the set of regular controls is not necessarily convex and the regular control enters the diffusion *** control problem is difficult to solve with the classical method of spike *** authors use the approach of relaxed controls to establish maximum principle for this stochastic optimal control *** optimality conditions are also investigated.

关键词： Forward-backward system maximum principle relaxed control singular control.

THEORY AND APPLICATION OF FRACTIONAL STEP CHARACTERISTIC FINITE DIFFERENCE METHOD IN NUMERICAL SIMULATION OF SECOND ORDER ENHANCED OIL PRODUCTION

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Acta Mathematica Scientia 2015年第6期35卷 1547-1565页

作者：袁益让程爱杰羊丹平李长峰 Institute of Mathematics Shandong University School of economics Shandong University

A kind of second-order implicit fractional step characteristic finite difference method is presented in this paper for the numerically simulation coupled system of enhanced （chemical） oil production in porous media. Some techniques, such as the calculus of variations, energy analysis method, commutativity of the products of difference operators, decomposition of high-order difference operators and the theory of a priori estimates are introduced and an optimal order error estimates in l^2 norm is derived. This method has been applied successfully to the numerical simulation of enhanced oil production in actual oilfields, and the simulation results ate quite interesting and satisfactory.

关键词： enhanced (chemical) oil production three-dimensional porous coupled system second-order implicit characteristic fractional step differences optimal order l^2 estimate application in actual oilfields

CONVERGENCE ANALYSIS OF MIXED VOLUME ELEMENT-CHARACTERISTIC MIXED VOLUME ELEMENT FOR THREE-DIMENSIONAL CHEMICAL OIL-RECOVERY SEEPAGE COUPLED PROBLEM

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Acta Mathematica Scientia 2018年第2期38卷 519-545页

作者：袁益让程爱杰羊丹平李长峰杨青 Institute of Mathematics Shandong University School of economics Shandong University

The physical model is described by a seepage coupled system for simulating numerically three-dimensional chemical oil recovery, whose mathematical description includes three equations to interpret main concepts. The pressure equation is a nonlinear parabolic equation, the concentration is defined by a convection-diffusion equation and the saturations of different components are stated by nonlinear convection-diffusion equations. The transport pressure appears in the concentration equation and saturation equations in the form of Darcy velocity, and controls their processes. The flow equation is solved by the conservative mixed volume element and the accuracy is improved one order for approximating Darcy velocity. The method of characteristic mixed volume element is applied to solve the concentration, where the diffusion is discretized by a mixed volume element method and the convection is treated by the method of characteristics. The characteristics can confirm strong computational stability at sharp fronts and it can avoid numerical dispersion and nonphysical oscillation. The scheme can adopt a large step while its numerical results have small time-truncation error and high order of accuracy. The mixed volume element method has the law of conservation on every element for the diffusion and it can obtain numerical solutions of the concentration and adjoint vectors. It is most important in numerical simulation to ensure the physical conservative nature. The saturation different components are obtained by the method of characteristic fractional step difference. The computational work is shortened greatly by decomposing a three-dimensional problem into three successive one-dimensional problems and it is completed easily by using the algorithm of speedup. Using the theory and technique of a priori estimates of differential equations, we derive an optimal second order estimates in 12 norm. Numerical examples are given to show the effectiveness and practicability and the m

关键词： Chemical oil recovery mixed volume element-characteristic mixed volume element characteristic fractional step differences local conservation of mass second-order error estimate in l2-norm

Modified characteristic finite difference fractional step method formoving boundary value problem of percolation coupled system

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Applied Mathematics and Mechanics(English Edition) 2012年第2期33卷 177-194页

作者：袁益让李长峰孙同军 Institute of Mathematics Shandong University School of economics Shandong University

For the coupled system with moving boundary values of multilayer dynamicsof fluids in porous media,a characteristic finite difference fractional step scheme appli-cable to the parallel arithmetic is put *** techniques,such as the change ofregions,the calculus of variations,the piecewise threefold quadratic interpolation,themultiplicative commutation rule of difference operators,the decomposition of high orderdifference operators,and the prior estimates,are *** optimal order estimatesin the l2norm are derived to determine the error in the approximate *** nu-merical method has been successfully used to simulate the flow of migration-accumulationof the multilayer percolation coupled *** numerical results are well illustratedin this paper.

关键词： multilayer percolation coupled system moving boundary value charac-teristic fractional finite difference optimal order error estimate numerical simulation ofenergy source

A Class of Backward Doubly Stochastic Differential Equations with Discontinuous Coefficients

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Acta Mathematicae Applicatae Sinica 2014年第4期30卷 965-976页

作者： Qing-feng ZHU Yu-feng SHI School of Mathematic and Quantitative economics Shandong University of Finance and Economics Institute for Financial Studies and School of Mathematics Shandong University School of Statistics Shandong University of Finance and Economics

In this work the existence of solutions of one-dimensional backward doubly stochastic differential equations （BDSDEs） with coefficients left-Lipschitz in y （may be discontinuous） and Lipschitz in z is studied. Als... 详细信息

关键词： backward doubly stochastic differential equations backward stochastic integral comparisontheorem

Modified characteristic finite difference fractional step method for moving boundary value problem of nonlinear percolation system

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Applied Mathematics and Mechanics(English Edition) 2013年第4期34卷 417-436页

作者：袁益让李长峰孙同军刘允欣 Institute of Mathematics Shandong University School of economics Shandong University

A fractional step scheme with modified characteristic finite differences run- ning in a parallel arithmetic is presented to simulate a nonlinear percolation system of multilayer dynamics of fluids in a porous medium with moving boundary values. With the help of theoretical techniques including the change of regions, piecewise threefold quadratic interpolation, calculus of variations, multiplicative commutation rule of differ- ence operators, multiplicative commutation rule of difference operators, decomposition of high order difference operators, induction hypothesis, and prior estimates, an optimal order in 12 norm is displayed to complete the convergence analysis of the numerical algo- rithm. Some numerical results arising in the actual simulation of migration-accumulation of oil resources by this method are listed in the last section.

关键词： multilayer nonlinear percolation system moving boundary values modified characteristic fractional finite difference optimal order convergence analysis numerical simulation of energy source

Kernel-blending connection approximated by a neural network for image classification

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Computational Visual Media 2020年第4期6卷 467-476页

作者： Xinxin Liu Yunfeng Zhang Fangxun Bao Kai Shao Ziyi Sun Caiming Zhang shandong university of Finance and economics Jinan 250014China shandong university Jinan 250100China

This paper proposes a kernel-blending connection approximated by a neural network(KBNN)for image classification.A kernel mapping connection structure,guaranteed by the function approximation theorem,is devised to blend feature extraction and feature classification through neural network ***,a feature extractor learns features from the raw ***,an automatically constructed kernel mapping connection maps the feature vectors into a feature ***,a linear classifier is used as an output layer of the neural network to provide classification ***,a novel loss function involving a cross-entropy loss and a hinge loss is proposed to improve the generalizability of the neural *** results on three well-known image datasets illustrate that the proposed method has good classification accuracy and generalizability.

关键词： image classification blending neural network function approximation kernel mapping connection generalizability