关于受控扩散过程的动力学

On the Dynamics of Controlled Diffusions

主要考虑在给定初始条件下构形变量的时间演化可由受控扩散描述的有限自由度动力系统.基于随机控制一般理论,引入受控扩散的随机作用量的两个适当形式.通过离散该随机作用量,导出系统受控扩散的广义坐标表示的动力学方程,该方程连同连续方程一起精确描述扩散运动的概率进程.

Treats of dynamical systems with finite number of degrees of freedom such that the time evolution of the configuration variables for given initial conditions can well be described by controlled diffusions.Two suitable forms of stochastic action associated with the controlled diffusions are introduced in the general framework of stochastic control theory.By discretizing the stochastic action,the dynamical equations for the controlled diffusions of the given systems are derived in terms of generalized coordinates.These equations,together with the continuity equation,describe exactly the probability approach of the diffusion motion.