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MULTI-DIMENSIONAL REFLECTED BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS AND THE COMPARISON THEOREM

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Acta Mathematica Scientia 2010年第5期30卷 1819-1836页

作者：吴臻消华 school of mathematics Shandong University school of mathematics and Statistics Shandong University at Weihai

In this article, we study the multi-dimensional reflected backward stochastic differential equations. The existence and uniqueness result of the solution for this kind of equation is proved by the fixed point argument where every element of the solution is forced to stay above the given stochastic process, i.e., multi-dimensional obstacle, respectively. We also give a kind of multi-dimensional comparison theorem for the reflected BSDE and then use it as the tool to prove an existence result for the multi-dimensional reflected BSDE where the coefficient is continuous and has linear growth.

关键词： backward stochastic differential equations comparison theorem local time

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

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.

The minimal sublinear expectations and their related properties

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Science china mathematics 2009年第4期52卷 785-793页

作者： JIA GuangYan school of mathematics, shandong university, jinan 2.0100, china 1. school of mathematics Shandong University Jinan 250100 China

In this paper, we prove that for a sublinear expectation ?[·] defined on L 2(Ω, $ \mathcal{F} $ ), the following statements are equivalent: ? is a minimal member of the set of all sublinear expectations defined on L 2(Ω, $ \mathcal{F} $ )? is linearthe two-dimensional Jensen’s inequality for ? holds.Furthermore, we prove a sandwich theorem for subadditive expectation and superadditive expectation.

关键词： g-expectation Jensen’s inequality linear expectation subadditive expectation sublinear expectation 60H10

Adaptive bidirectional diffusion for image restoration

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Science china(Information Sciences) 2010年第12期53卷 2452-2460页

作者： FU ShuJun 1,2 & ZHANG CaiMing 1 1 school of Computer Science and Technology, shandong university, jinan 250101, china 2.school of mathematics, shandong university, jinan 2.0100, china 1. school of Computer Science and Technology Shandong University Jinan 250101 China2. School of Mathematics Shandong University Jinan 250100 China

A large number of applications in image processing and computer vision depend on image quality. In this paper, combining the forward diffusion with the backward diffusion by different weights, we present an adaptive bidirectional diffusion method for image denoising and deblurring simultaneously. Further, we introduce a gradient factor into the data fidelity term, which forms a spatially varying constraint and allows a better restoration of image edges and fine details. In order to obtain a stable solution, we develop a numerically stable scheme and give its theoretical analysis. Finally, we show advantages of this method in deblurring edges, denoising and restoring fine details of image compared with other related methods in experiments.

关键词： image restoration bidirectional diffusion inverse diffusion anisotropic diffusion stabilizing scheme spatially varying constraint

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 1. school of mathematics Shandong University Jinan 250100 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

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 250100 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

Construction of convex solutions for the second type of Feigenbaum's functional equations

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Science china mathematics 2009年第8期52卷 1617-1638页

作者： SI JianGuo & ZHANG Min school of mathematics, shandong university, jinan 2.0100, china school of mathematics Shandong University Jinan 250100 China

In this paper, convex solutions for the second type of Feigenbaum's equation f (x) = λ1 f (f (λx)), 0 < λ < 1, f (0) = 1, 0 f (x) 1, x ∈ [0, 1] are investigated. Using constructive methods, we discuss the existenc... 详细信息

In this paper, convex solutions for the second type of Feigenbaum's equation f (x) = λ1 f (f (λx)), 0 2-convex solutions of the above equation.

关键词： the second type of Feigenbaum’s functional equations constructive method initial function convex solutions

Mechanical model of vulnerable atherosclerotic plaque rupture

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Science china(Physics,Mechanics & Astronomy) 2004年第4期47卷 452-462页

作者： SU Haijun1, ZHANG Mei2 & ZHANG Yun2 1. school of mathematics and System Science, shandong university, jinan 2.0100, china 2. Qilu Hospital, shandong university, jinan 250012, china 1. school of mathematics and System Science Shandong University 250100 Jinan China 2. Qilu Hospital Shandong University 250012 Jinan China

Rupture of atherosclerotic plaque is the main trigger of acute cardiovascular events, but the mechanism of plaque rupture is still unknown. We have constructed a model describing the motion of the fibrous cap of the plaque using the theory of elastic mechanics and studied the stability of the plaque theoretically. It has shown that plaque rupture is the result of a dynamic interplay between factors intrinsic to the plaque itself and extrinsic factors. We have proposed a new mechanism of plaque rupture, given a new explanation about the nonlinear dynamic progress of atherosclerosis and suggested a method to identify the vulnerable plaques to manage atherosclerosis.

关键词： fibrous cap, parametric resonance, stability, mechanism, identification.

A general central limit theorem under sublinear expectations

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Science china mathematics 2010年第8期53卷 1989-1994页

作者： LI Min & SHI YuFeng school of mathematics,shandong university,jinan 2.0100,china 1. school of mathematics Shandong University Jinan 250100 China

Under some weaker conditions,we give a central limit theorem under sublinear expectations,which extends Peng's central limit theorem.

关键词： central limit theorem sublinear expectation G-normal distribution