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LEAST-SQUARES MIXED FINITE ELEMENT METHODS FOR NONLINEAR PARABOLIC PROBLEMS

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Journal of Computational mathematics 2002年第2期20卷 153-164页

作者： Dan-ping yang (School of mathematics and system Science, shandong university, jinan 2.0100, china) School of mathematics and system Science Shandong University Jinan 250100

Focuses on the formulation of a number of least-squares mixed finite element schemes to solve the initial boundary value problem of a nonlinear parabolic partial differential equation. Convergence analysis; Informatio... 详细信息

关键词： least-squares algorithm mixed finite element nonlinear parabolic problems convergence analysis

ON JENSEN'S INEQUALITY FOR g-EXPECTATION

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Chinese Annals of mathematics,Series B 2004年第3期25卷 401-412页

作者： JIANG LONG CHEN ZENGJING School of mathematics and system sciences, shandong university, jinan 2.0100, china. Department of mathematics, china university of Mining and Technology, Xuzhou 221008, Jiangsu,china. E-mail: jianglong@*** School of mathematics and system sciences, shandong university, jinan 2.0100, china. School of mathematics and system sciences Shandong University Jinan 250100 China Department of mathematics China University of Mining and Technology Xuzhou 221008 Jiangsu China

Briand et al. gave a counterexample showing that given g, Jensen's inequality for g-expectation usually does not hold in general This paper proves that Jensen's inequality for g-expectation holds in general if and onl... 详细信息

关键词： Backward stochastic differential equation Jensen's inequality g-expectaation Conditional g-expectation Comparison theorem

Limit theorem and uniqueness theorem of backward stochastic differential equations

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Science china mathematics 2006年第10期49卷 1353-1362页

作者： JIANG Long Department of mathematics, china university of Mining and Technology, Xuzhou 221008, china Institute of mathematics, Fudan university, Shanghai 200433, china School of mathematics and system sciences, shandong university, jinan 2.0100, china Department of mathematics China University of Mining and Technology Xuzhou China Institute of mathematics Fudan University Shanghai China School of mathematics and system sciences Shandong University Jinan China

This paper establishes a limit theorem for solutions of backward stochastic differential equations (BSDEs). By this limit theorem, this paper proves that, under the standard assumption g(t,y,0) = 0, the generator g of a BSDE can be uniquely determined by the corresponding g-expectationεg;this paper also proves that if a filtration consistent expectation S can be represented as a g-expectationεg, then the corresponding generator g must be unique.

关键词： backward stochastic differential equation, g-expectation, generator.

An exact solution for flow past an accelerated horizontal plate in a rotating fluid with the generalized Oldroyd-B model

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Acta Mechanica Sinica 2009年第4期25卷 463-469页

作者： Jianhong Kang Mingyu Xu Institute of Applied mathematics,School of mathematics and system Science,shandong university, 2.0100 jinan, china Institute of Applied mathematics School of Mathematics and System Science Shandong University Jinan China

In this paper, the generalized Oldroyd-B with fractional calculus approach is used. An exact solution in terms of Fox-H function for flow past an accelerated horizontal plate in a rotating fluid is obtained by using discrete Laplace transform method. A comparison among the influence of various parameters in the Oldroyd-B model and the angular velocity of the fluid on the velocity profiles is made through numerical method in graphic form.

关键词： Generalized Oldroyd-B model Rotating fluid Accelerated plate Exact solution

Jensen's Inequality for Backward Stochastic Differential Equations

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Chinese Annals of mathematics,Series B 2006年第5期27卷 553-564页

作者： Long JIANG Department of mathematics, china university of Mining and Technology, Xuzhou 221008, Jiangsu, china School of Mathematical sciences, Fudan university, Shanghai 200433, china School of mathematics and system sciences, shandong university, jinan 2.0100, china. Department of mathematics China University of Mining and Technology Xuzhou 221008 Jiangsu China School of Mathematical sciences Fudan University Shanghai 200433 China School of mathematics and system sciences Shandong University Jinan 250100 China

Under the Lipschitz assumption and square integrable assumption on g, the author proves that Jensen＇s inequality holds for backward stochastic differential equations with generator g if and only if g is independent of y, g（t, 0）≡ 0 and g is super homogeneous with respect to z. This result generalizes the known results on Jensen＇s inequality for gexpectation in [4, 7-9].

关键词： Backward stochastic differential equation g-Expectation Jensen's inequality for g-expectation Jensen's inequality for BSDEs

S-rough sets and knowledge separation

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Journal of systems Engineering and Electronics 2005年第2期16卷 403-410页

作者： Shi Kaiquan 1,21. School of mathematics and system sciences, Liaocheng university, Liaocheng 252059, P. R. china 2. School of mathematics and system sciences, shandong university, jinan 2.0100, P. R. china School of mathematics and system sciences Liaocheng University Liaocheng 252059 P. R. China School of mathematics and system sciences Shandong University Jinan 250100 P. R. China

The conceptions of the knowledge screen generated by S-rough sets are given: f- screen and - screen , and then puts forward - filter theorem, - filter theorem of knowledge. At last, the applications of knowledge separ... 详细信息

关键词： S- rough sets f- screen - screen f-filter theorem - filter theorem knowledge separation.

ON SOME RESULTS OF YI AND THEIR APPLICATIONS IN THE FUNCTIONAL EQUATIONS

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Acta Mathematica Scientia 2010年第5期30卷 1649-1660页

作者：杨连中张继龙 School of mathematics and system sciences Shandong University LMIB and School of mathematics and system sciences Beihang University

In this article, we establish some uniqueness theorems that improves some results of H. X. Yi for a family of meromorphic functions, and as applications, we give some results about the non-existence of meromorphic sol... 详细信息

关键词： functional equations meromorphic functions uniqueness

MAXIMUM PRINCIPLE FOR FORWARD-BACKWARD STOCHASTIC CONTROL system WITH RANDOM JUMPS AND APPLICATIONS TO FINANCE

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Journal of systems Science & Complexity 2010年第2期23卷 219-231页

作者： Jingtao SHI·Zhen WU School of mathematics,shandong university,jinan 2.0100,china. School of mathematics Shandong University Jinan China

Both necessary and sufficient maximum principles for optimal control of stochastic systemwith random jumps consisting of forward and backward state variables are *** control variableis allowed to enter both diffusion and jump *** result is applied to a mean-varianceportfolio selection mixed with a recursive utility functional optimization *** expressionof the optimal portfolio selection strategy is obtained in the state feedback form.

关键词： Forward-backward stochastic control system maximum principle Poisson random measure recursive utility stochastic optimal control.

A maximum principle for partially observed optimal control of forward-backward stochastic control systems

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Science china(Information sciences) 2010年第11期53卷 2205-2214页

作者： WU Zhen School of mathematics, shandong university, jinan 2.0100, china School of mathematics Shandong University Jinan China

This paper studies an optimal control problem for partially observed forward-backward stochastic control system with a convex control domain and the forward diffusion term containing control variable. A maximum principle is proved for this kind of partially observable optimal control problems and the corresponding adjoint processes are characterized by the solutions of certain forward-backward stochastic differential equations in finite-dimensional spaces. One partially observed recursive linear-quadratic (LQ) optimal control example is also given to show the application of the obtained maximum principle. An explicit observable optimal control is obtained in this example.

关键词： maximum principle partial information adjoint equation backward stochastic differential equation filtering linear-quadratic optimal control