Linear-Quadratic Optimal Control Problems for Mean-Field Stochastic Differential Equation with Lévy Process

This paper investigates a linear-quadratic mean-field stochastic optimal control problem under both positive definite case and indefinite case where the controlled systems are mean-field stochastic differential equations driven by a Brownian motion and Teugels mar-tingales associated with Lévy processes.In either case,we obtain the optimality system for the optimal controls in open-loop form,and by means of a decoupling technique,we obtain the optimal controls in closed-loop form which can be represented by two Riccati differen-tial equations.Moreover,the solvability of the optimality system and the Riccati equations are also obtained under both positive definite case and indefinite case.

A Mean-Field Linear-Quadratic Stochastic Stackelberg Differential Game with one Leader and Two Followers

This paper is concerned with a linear-quadrati stochastic Stackelberg differential game with one leader and two followers,where the game system is governed by a mean-field stochastic differential equatio.By maximum principle and verification theorem,the open-loop Stackelberg solution is expressed as a feedback form of the state and its mean with the help of three systems of Riccati equations.

表征论与动力系统理论之争中的表征饥饿问题

当前认知科学的主流研究范式已经从离身认知转向具身认知。然而表征主义者一直试图尝试挽回表征在认知科学中的地位与作用,其中最具代表性的思潮便是表征饥饿问题。尽管有批评者认为表征饥饿概念模糊,并试图用新的研究范式,如动力系统理论(DST)来解释表征饥饿现象,但表征主义者依然尝试把DST纳入表征系统,将认知过程看成一个具有多层次、整体性、动态性、协同性特征的反馈控制系统,是一个由非表征、适度表征、完全表征、表征饥饿构成的统一体,而不是严格的二元式对立来进行回应。因而由于表征饥饿问题的存在,彻底取消表征仍然是存疑的。