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Optimal variational principle for backward stochastic control systems associated with Lévy processes

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Science china Mathematics 2012年第4期55卷 745-761页

作者： TANG MaoNing 1 & ZHANG Qi 2,1 Department of mathematical sciences,Huzhou university,Huzhou 313000,china 2 school of mathematical sciences,fudan university,shanghai 200433,china Department of mathematical sciences Huzhou University Huzhou China school of mathematical sciences Fudan University Shanghai China

The paper is concerned with optimal control of backward stochastic differentiM equation （BSDE） driven by Teugel＇s martingales and an independent multi-dimensional Brownian motion, where Teugel＇s martingales are a family of pairwise strongly orthonormal martingales associated with L6vy processes （see e.g., Nualart and Schoutens＇ paper in 2000）. We derive the necessary and sufficient conditions for the existence of the optimal control by means of convex variation methods and duality techniques. As an application, the optimal control problem of linear backward stochastic differential equation with a quadratic cost criteria （or backward linear-quadratic problem, or BLQ problem for short） is discussed and characterized by a stochastic Hamilton system.

关键词： stochastic control stochastic maximum principle Ldvy processes Teugel's martingales backwardstochastic differential equations

Local 3-cocycles of von Neumann algebras

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Science china Mathematics 2007年第9期50卷 1240-1250页

作者： Cheng-jun HOU~(1+) Ben-yin FU~2 1 school of mathematical sciences,Qufu Normal university,Qufu 273165,china 2 school of mathematical sciences,fudan university,shanghai 200433,china school of mathematical sciences Qufu Normal University Qufu China school of mathematical sciences Fudan University Shanghai China

We show that every local 3-cocycle of a von Neumann algebra $\mathcal{R}$ into an arbitrary unital dual $\mathcal{R}$ -bimodule $\mathcal{S}$ is a 3-cocycle.

关键词： von Neumann algebra dual bimodule local 3-cocycle 3-cocycle 46L10

Riemann boundary value problems and reflection of shock for the Chaplygin gas

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Science china Mathematics 2012年第4期55卷 671-685页

作者： CHEN ShuXing 1,& QU AiFang 2 1 school of mathematical sciences,fudan university,shanghai 200433,china 2 Wuhan Institute of Physics and Mathematics,Chinese Academy of sciences,Wuhan 430071,china school of mathematical sciences Fudan University Shanghai China Wuhan Institute of Physics and Mathematics Chinese Academy of Sciences Wuhan China

In this paper,we study two-dimensional Riemann boundary value problems of Euler system for the isentropic and irrotational Chaplygin gas with initial data being two constant states given in two sectors respectively,where one sector is a quadrant and the other one has an acute vertex *** prove that the Riemann boundary value problem admits a global self-similar solution,if either the initial states are close,or the smaller sector is also near a *** result can be applied to solving the problem of shock reflection by a ramp.

关键词： Riemann boundary value problem reflection of shock Chaplygin gas wave interaction Eulersystem

Connectivity of the Mandelbrot set for the family of renormalization transformations

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Science china Mathematics 2010年第3期53卷 849-862页

作者： WANG XiaoGuang 1,QIU WeiYuan 1 , YIN YongCheng 1 , QIAO JianYong 2 & GAO JunYang 2 1 school of mathematical sciences, fudan university, shanghai 200433, china 2 Center of Mathematics, china university of Mining and Technology, Beijing 100083, china school of mathematical sciences Fudan University Shanghai China Center of Mathematics China University of Mining and Technology Beijing China

We show that the Mandelbrot set for the family of renormalization transformations of 2-dimensional diamond-like hierachical Potts models in statistical mechanics is connected. We also give an upper bound for the Hausd... 详细信息

关键词： connectivity Mandelbrot set renormalization transformations

Thompson's Group and the Linear Group GL∞（Z）

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Chinese Annals of Mathematics,Series B 2011年第6期32卷 863-884页

作者： Yan WU 1 Xiaoman CHEN 21 College of Mathematics Physics and Information Engineering,Jiaxing university,Jiaxing 314033,Zhejiang,china.2 school of mathematical sciences,fudan university,shanghai 200433,china.

The authors study the finite decomposition complexity of metric spaces of H,equipped with different metrics,where is a subgroup of the linear group GL∞ (Z).It is proved that there is an injective Lipschitz mapφ:(F,ds) → (H,d),where is the Thompson's group,the word-metric of with respect to the finite generating set and a metric of *** it is not a proper ***,it is proved that:φ(F,ds) → (H,d1) is not a Lipschitz map,where d1 is another metric of H.

关键词： Finite decomposition complexity Thompson’s group Word-metric Lipschitz map Reduced tree diagram

On the equivalence of extremal Teichmller mapping

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Science china Mathematics 2009年第1期52卷 77-86页

作者： FAN JinHua1 & CHEN JiXiu2 1 Department of Applied Mathematics, Nanjing university of Science and Technology, Nanjing 210094, china 2 school of mathematical sciences, fudan university, shanghai 200433, china

Let T(△) and B(△) be the Teichmuller space and the infinitesimal Teichmuller space of the unit disk △ respectively. In this paper, we show that [ν]B(△) being an infinitesimal Strebel point does not imply that [ν... 详细信息

关键词： Teichmuller space infinitesimal Teichmu¨ller space Strebel point

The fundamental solution of the Keldysh typeoperator

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Science china Mathematics 2009年第9期52卷 1829-1843页

作者： CHEN ShuXing school of mathematical sciences, fudan university, shanghai 200433, china school of mathematical sciences Fudan University Shanghai China

In this paper we discuss the fundamental solution of the Keldysh type operator $ L_\alpha u \triangleq \frac{{\partial ^2 u}} {{\partial x^2 }} + y\frac{{\partial ^2 u}} {{\partial y^2 }} + \alpha \frac{{\partial u}} {{\partial y}} $ , which is a basic mixed type operator different from the Tricomi operator. The fundamental solution of the Keldysh type operator with $ \alpha > - \frac{1} {2} $ is obtained. It is shown that the fundamental solution for such an operator generally has stronger singularity than that for the Tricomi operator. Particularly, the fundamental solution of the Keldysh type operator with $ \alpha < \frac{1} {2} $ has to be defined by using the finite part of divergent integrals in the theory of distributions.

关键词： mixed type equation Keldysh operator fundamental solution finite part of divergent integral 35M10 35A08

Local Existence of Smooth Solutions to the FENE Dumbbell Model

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Chinese Annals of Mathematics,Series B 2012年第4期33卷 501-520页

作者： Ge YANG11school of mathematical sciences, fudan university, shanghai 200433, china. school of mathematical sciences Fudan University Shanghai China

The author proves the local existence of smooth solutions to the finite extensible nonlinear elasticity (FENE) dumbbell model of polymeric flows in some weighted spaces if the non-dimensional parameter b > 2.

关键词： Fokker-Planck equation FENE model Degenerate parabolic equations Regularity

RADIAL BASIS FUNCTION INTERPOLATION IN SOBOLEV SPACES AND ITS APPLICATIONS

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Journal of Computational Mathematics 2007年第2期25卷 201-210页

作者： Manping Zhang (school of mathematical sciences,fudan university,shanghai 200433,china Institute of Computational Mathematics,Chinese Academy of sciences,Beijing 100080,china school of mathematical sciences fudan university Shanghai 200433

In this paper we study the method of interpolation by radial basis functions and give some error estimates in Sobolev space H^k（Ω）（k 〉 1）. With a special kind of radial basis function, we construct a basis in H^k（Ω） and derive a meshless method for solving elliptic partial differential equations. We also propose a method for computing the global data density.

关键词： Sobolev space Radial basis function Global data density Meshless method