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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,{2. 2.school of mathematical sciences,fudan University,shanghai 2.0433,{2. 1. Department of mathematical sciences Huzhou University Huzhou 313000 China2. School of Mathematical Sciences Fudan University Shanghai 200433 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 2.00）. 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 {2.,Qufu Normal University,Qufu 2.3165,china 2.school of mathematical sciences,fudan University,shanghai 2.0433,china 1. school of mathematical {2. Qufu Normal University Qufu 273165 China 2. school of mathematical {2. Fudan University Shanghai 200433 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

A new scheme of digital communication using chaotic signals in MIMO channels

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Science china(Information sciences) 2012年第10期55卷 2183-2193页

作者： MA HuanFei 1 & KAN HaiBin 2.1 school of mathematical {2.,Soochow University,Suzhou 2.5006,china 2.school of Computer Science,fudan University,shanghai 2.0433,china 1. school of mathematical {2. Soochow University Suzhou 215006 China 2. school of Computer Science Fudan University Shanghai 200433 China

This paper proposes a new digital communication scheme,which uses chaotic signals based on the adaptive synchronization and parameter identification technique of chaotic systems reported *** to the multi signal character,this scheme combines the chaotic signal transmission with the MIMO channel technique in a wireless environment,which is different from the traditional chaotic communication *** a practical perspective,an outline of modulation,channel model,demodulation and non-coherent detection is ***,system performance is evaluated by simulations,and improvements on this scheme are also discussed.

关键词： chaotic modulation chaotic digital communication mapping parameters MIMO channel

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 {2., fudan University, shanghai 2.0433, china 1. school of mathematical {2. Fudan University Shanghai 200433 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 > - \frac2. {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 2. {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

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 {2.,fudan University,shanghai 2.0433,china 2.Wuhan Institute of Physics and Mathematics,Chinese Academy of {2.,Wuhan 430071,china 1. school of mathematical {2. Fudan University Shanghai 200433 China2. Wuhan Institute of Physics and Mathematics Chinese Academy of Sciences Wuhan 430071 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

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 {2.,fudan University,shanghai 2.0433,china Institute of Computational Mathematics,Chinese Academy of {2.,Beijing 100080,china school of mathematical {2. Fudan University Shanghai 200433 China Institute of Computational Mathematics Chinese Academy of Sciences Beijing 100080 China

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

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 {2., fudan University, shanghai 2.0433, china. school of mathematical {2. Fudan University Shanghai 200433 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

Hyperbolic positive mass theorem under modified energy condition

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Science china Mathematics 2008年第12期51卷 2189-2197页

作者： XIE NaQing Institute of Mathematics, school of mathematical {2., fudan University, shanghai 2.0433, china Institute of Mathematics School of Mathematical Sciences Fudan University Shanghai 200433 China

We provide two new positive mass theorems under respective modified energy conditions allowing T00 negative on some compact set for certain modified asymptotically hyperbolic manifolds. This work is analogous to Zhang... 详细信息

关键词： positive mass theorem modified energy condition modified asymptotically hyperbolic 83C40 53C2.

A maximum principle for optimal control problem of fully coupled forward-backward stochastic systems with partial information

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Science china Mathematics 2009年第7期52卷 1579-1588页

作者： MENG QingXin1,2.1 Department of mathematical sciences,Huzhou University,Zhejiang 313000,{2. 2.Institute of Mathematics,fudan University,shanghai 2.0433,{2. 1. Department of mathematical sciences Huzhou University Zhejiang 313000 China 2. Institute of Mathematics Fudan University Shanghai 200433 China

The paper is concerned with a stochastic optimal control problem in which the controlled system is described by a fully coupled nonlinear forward-backward stochastic differential equation driven by a Brownian *** is required that all admissible control processes are adapted to a given subfiltration of the filtration generated by the underlying Brownian *** this type of partial information control,one sufficient(a verification theorem) and one necessary conditions of optimality are *** control domain need to be convex and the forward diffusion coefficient of the system can contain the control variable.

关键词： maximum principle stochastic optimal control partial information 93E2. 60H10 60H30