Mathematical Sciences: Topics in Stochastic Control and Random Media

这一建议涉及随机控制理论和随机介质中波的多次散射的数学问题。它是这一领域两位知名专家周教授和梅纳尔迪共同努力的产物。主要的研究工作将集中在研究随机控制问题的各种理论问题上。假定动态过程受随机信号的影响。目标是确定优化特定目标的控制函数，该函数表示为关于过程轨迹的函数。该控件应该具有冲动型特征。这是物理情况的理想化版本，人们可以观察到过程轨迹的突然变化，这可以被认为是不连续或跳跃。例如，仓库中的库存库存可以这样表示，因为它们在交付新库存时经历了价值的跃升。脉冲性质的控制通常用狄拉克分布来表示。这种脉冲的定时和质量是一个人想要以最佳方式选择的控制参数。

This proposal is concerned with the mathematical problems of stochastic control theory and multiple scattering of waves in random media. It is a product of joint efforts of two known specialists in this area, Professors Chow and Menaldi. The main research effort will be invested in the study of various theoretical issues in the stochastic control problems. It is assumed that dynamical process is subject to influence of random signals. The goal is to determine a control function that optimizes a certain objective, expressed as a function on process trajectories. The control is supposed to have an impulse character. This is an idealized version of a physical situation where one can observe abrupt changes inprocess trajectories, which can be thought of as discontinuities, or jumps. Fo example, the inventory stocks in a warehouse may be represented in this way, as they experience a jump in the value at the delivery of new stock. The control of an impulse nature is usually represented mathematically by Dirac distributions. The timings and masses of such impulses are the control parameters that one wants to select in an optimal fashion.