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Boundedness of a Derived Function of a Solution About a Class of Diffusion variational equations

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Acta Mathematica Sinica,English Series 2004年第3期20卷 463-474页

作者： KunHuiLIU CollegeofScience BeijingJiaotongUniversityBeijing100044P.R.China

In this paper the boundedness of a derived function of a solution about a class of diffusion variational equations is discussed. The application of it to related stochastic analysis problems is also illustrated. What should be emphasized is that the problem discussed and the ways proved in this paper are fundamentally new and the conclusion of this paper is fairly profound.

关键词： variational equation Diffusion equation Classical solution Boundedness Stochastic analysis

Construction of the Solution of variational equations for constrained Birkhoffian systems

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Chinese Physics B 2002年第5期11卷 437-440页

作者：张毅 DepartmentofUrbanConstruction UniversityofScienceandTechnologyofSuzhouSuzhou215011China

In this paper we present the variational equations of constrained Birkhoffian systems and study their solution. Itis proven that, under some conditions, a particular solution of variational equations can be obtained b... 详细信息

关键词： analytical mechanics constrained Birkhoffian system variational equation first integral

The Optimal Control of Fully-Coupled Forward-Backward Doubly Stochastic Systems Driven by Ito-Lévy Processes

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Journal of Systems Science & Complexity 2019年第4期32卷 997-1018页

作者： WANG Wencan WU Jinbiao LIU Zaiming School of Control Science and Engineering Shandong UniversityJinan 250061China School of Mathematics and Statistics Central South UniversityChangsha 410083China

This paper studies the optimal control of a fully-coupled forward-backward doubly stochastic system driven by Ito-Lévy processes under partial *** existence and uniqueness of the solution are obtained for a type of fully-coupled forward-backward doubly stochastic differential equations(FBDSDEs in short).As a necessary condition of the optimal control,the authors get the stochastic maximum principle with the control domain being convex and the control variable being contained in all *** proposed results are applied to solve the forward-backward doubly stochastic linear quadratic optimal control problem.

关键词： Forward-backward doubly stochastic differential equations Ito-Lévy processes linear quadratic problem maximum principle variational equation

Pointwise Second-Order Necessary Conditions for Stochastic Optimal Control with Jump Diffusions

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Communications in Mathematics and Statistics 2023年第4期11卷 741-766页

作者： Abdelhak Ghoul Mokhtar Hafayed Imad Eddine Lakhdari Shahlar Meherrem Laboratory of Mathematical Analysis Probabilities and OptimizationsUniversity of BiskraPo Box 14507000 BiskraAlgeria Department of Mathematics Yasar UniversityUniversity avenAgaclıYol No.35-57IzmirTurkey

In this paper,we establish a second-order necessary conditions for stochastic optimal control for jump *** controlled system is described by a stochastic differential systems driven by Poisson random measure and an independent Brownian *** control domain is assumed to be *** second-order maximum principle for controlled jump diffusion in terms of the martingale with respect to the time variable is *** proof of the main result is based on variational approach using the stochastic calculus of jump diffusions and some estimates on the state processes.

关键词： Optimal control Stochastic systems with jumps Pointwise second-order necessary condition Maximum principle variational equation

SOLUTION OF GENERALIZED COORDINATE FOR WARPING FOR NATURALLY CURVED AND TWISTED BEAMS

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Applied Mathematics and Mechanics(English Edition) 2004年第10期25卷 1166-1175页

作者：虞爱民易明 Key Laboratory of Solid Mechanics of MOE Tongji University Institute of Automobile Tongji University

A theoretical method for static analysis of naturally curved and twisted beams under complicated loads was presented, with special attention devoted to the solving process of governing equations which take into account the effects of torsion-related warping as well as transverse shear deformations. These governing equations, in special cases, can be readily solved and yield the solutions to the problem. The solutions can be used for the analysis of the beams, including the calculation of various internal forces, stresses, strains and displacements. The present theory will be used to investigate the stresses and displacements of a plane curved beam subjected to the action of horizontal and vertical distributed loads. The numerical results obtained by the present theory are found to be in very good agreement with the results of the FEM results. Besides, the present theory is not limited to the beams with a double symmetric cross-section, it can also be extended to those with arbitrary cross-sectional shape.

关键词： naturally curved and twisted beam St. Venant torsional warping function generalized coordinate for warping the minimum potential energy principal variational equation

A new class of impulse stochastic control models with non-negative control quantity

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Science China(Information Sciences) 2011年第3期54卷 638-652页

作者： LIU XiaoPeng & LIU KunHui College of Science, Beijing Jiaotong University, Beijing 100044, China College of Science Beijing Jiaotong University Beijing China

This paper advances and studies a new class of impulse stochastic control models. Its state structure is defined by a linear stochastic differential equation of the semi-martingale, its control cost function is a twovariable function of pre-control state quantity and control quantity, and its control quantity is kept non-negative. First this paper constructs a new type of variational equations and proves its solution exists. Using a series of stochastic analysis methods to research the solution function of this type of variational equations, this paper proves the existence of optimal control and analyzes its structure in depth. Because of the big difference between the model in this paper and stochastic control models in previous papers, the analysis method here is quite different from previous ones. It is expected that this paper will have important theoretical significance for stochastic control research, along with wide applicative value in finance control and security management.

关键词： impulse stochastic control control quantity variational equation optimal control semi-martingale

The generalization of a class of impulse stochastic control models of a geometric Brownian motion

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Science in China(Series F) 2009年第6期52卷 983-998页

作者： LIU XiaoPeng LIU KunHui College of Science Beijing Jiaotong University Beijing 100044 China

Recently, international academic circles advanced a class of new stochastic control models of a geometric Brownian motion which is an important kind of impulse control models whose cost structure is different from the others before, and it has a broad applying background and important theoretical significance in financial control and management of *** paper generalizes substantially the above stochastic control models under quite extensive conditions and describes the models more exactly under more normal theoretical system of stochastic *** establishing a set of proper variational equations and proving the existence of its solution, and applying the means of stochastic analysis, this paper proves that the generalized stochastic control models have optimal ***, we also analyze the structure of optimal controls ***, we study the solution function of variational equations in a relatively deep-going way, which constitutes the value function of control models to some *** the analysis methods of this paper are greatly different from those of original reference, this paper possesses considerable originality to some *** addition, this paper gives the strict proof to the part of original reference which is not fairly well-knit in analyses, and makes analyses and discussions of the model have the exactitude of mathematical sense.

关键词： mpulse stochastic control geometric Brownian motion variational equation optimal control

Stochastic global maximum principle for optimization with recursive utilities

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Probability, Uncertainty and Quantitative Risk 2017年第1期2卷 1-20页

作者： Mingshang Hu Zhongtai Institute of Finance Shandong UniversityJinanShandong 250100People’s Republic of China

In this paper,we study the recursive stochastic optimal control *** control domain does not need to be convex,and the generator of the backward stochastic differential equation can contain *** obtain the variational equations for backward stochastic differential equations,and then obtain the maximum principle which solves completely Peng’s open problem.

关键词： Backward stochastic differential equations Recursive stochastic optimal control Maximum principle variational equation

A Principal Theorem of Generalized Galerkin's Schemes

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Wuhan University Journal of Natural Sciences 2002年第2期7卷 137-138页

作者： Du Nai-lin 1, Du Nai-xia 2 1. School of Mathematics and Statistics, Wuhan University, Wuhan 430072, Hubei China 2. Hebei Institute of Architectural Science and Technology, Handan 056038, Hebei China School of Mathematics and Statistics Wuhan University Wuhan 430072 Hubei China Hebei Institute of Architectural Science and Technology Handan 056038 Hebei China

In the present paper, the authors announce a newlyproved theorem of theirs. This theorem is of principal significance to numerical computation of solutions of variational equations.

关键词： variational equation generalized Galerkin's scheme pseudoinverse