广义密度演化方程的δ函数序列解法

随机动力系统响应或状态向量的概率密度函数一般遵循概率密度演化方程，如Liouville方 程、FPK方程和Dostupov-Pugachev方程，但是上述方程均属于高维偏微分方程，求解相当 困难. 基于概率守恒原理的随机事件描述导出的广义密度演化方程，其维数与系统自由度无 关，为随机动力系统分析提供了可能的途径. 从广义密度演化方程的形式解出发，引入 δ函数的渐近序列，获得了广义密度演化方程的一种新的数值解法------广 义密度演化方程的δ序列解法. 将建议方法与非参数密度估计进行了对比， 指出非参数密度估计是该方法的一个特例. 最后，分别采用重构实例和演化实例验 证了该方法在一维和多维情形下的有效性.

SOLUTION OF GENERALIZED DENSITY EVOLUTION EQUATION VIA A FAMILY OF δ SEQUENCES

In the stochastic dynamics,it is one of the most important purposes to acquire the probability density function and its evolution process of the stochastic responses.The probability density function of the responses or state vector of a stochastic dynamical system is usually governed by some type of probability density evolution equations such as the Liouville,FPK or the Dostupov-Pugachev equation.However,these equations in high dimension are too hard to obtain the solutions.The generalized density evolutio...