在核反应堆弱中子源启动、安全控制过程中，人们特别希望能够快速评估系统内中子数密度、缓发中子先驱核及反应性的随机涨落行为，以及失控或严重事故等极端条件下的辐射剂量，便于反应堆安全分析和即时控制。在κ=κ(t)时，这种随机涨落现象不仅影响反应堆的启动时间，而且也会导致辐射剂量的随机性涨落。在k>1时，中子增殖及辐射剂量随机涨落的不确定性更大，对快中子反应堆，这一现象更为值得重视。俄罗斯科学家首先提出了用随机反应堆动力学方程来描述这一反应堆随机动力学现象的理论，即可描述反应堆内多群中子持续时间内的随机轨迹过程，又可讨论中子数的随机行为和源强对核安全影响的重要性。近年来在多学科领域已经兴起了应用随机微积分的数学方法来处理各种随机事件。本课题也拟研究用于处理反应堆随机动力学现象，其最大优势和特点是，可比MC方法能更快速地评估出反应堆的安全性，或发生事故时的辐射剂量。为此，我们将致力于这一方法的研究。

In the process of nuclear reactor start-up with a weak source and safety operation, in order to achieve the safety control of reactor, it is desirable to estimate in time random fluctuations in the neutron density, the delayed neutron precursor concentrations, and reactivity of the system, as well as to estimate the radiation dose in extreme conditions such as severe accident and loss of control. In case of κ=κ(t), the random fluctuations not only affect the reactor start-up time but also result in random fluctuations in radiation dose. In case of k>1, the uncertainties of random fluctuations in neutron multiplication and radiation dose are even greater, particularly for fast reactors for which this phenomenon deserves to be noted with more emphasis. The theory was first suggested by Russian scientists of using stochastic differential equation system to describe the stochastic dynamics of reactor. With this theory, we can describe the stochastic processes of neutrons with time, and estimate the influnce of this random behavior and the weak source on reactor safety. In recent years, stochastic mathematics has been widely used to deal with various kinds of random events in many fields. In this proposed research, we will use this method to study the stochastic dynamics of reactor. The biggest advantage of this method is that it is more efficient than Monte Carlo calculations for the estimations of reactor safety and radiation dose in case of accident.