| 概率密度演化理论的若干研究进展 |
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| 引用本文： | 李杰,陈建兵.概率密度演化理论的若干研究进展[J].应用数学和力学,2017,38(1):32-43. |
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| 作者姓名： | 李杰 陈建兵 |
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| 作者单位： | 同济大学 土木工程学院;土木工程防灾国家重点实验室(同济大学),上海 200092 |
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| 基金项目： | 国家自然科学基金(51538010;11672209） |
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| 摘 要： | 介绍了随机动力系统中概率密度演化理论的基本方程与求解方法〖CX4〗．〖CX〗在此基础上，论述了广义概率密度演化方程求解的若干新进展，包括群演化方程及其求解、概率空间剖分的理性准则、点集加密技术与信息拓展方法等.
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| 关 键 词： | 随机动力系统 概率密度演化理论 群演化 GF偏差 点集加密 |
| 收稿时间： | 2016-11-04 |
Some New Advances in the Probability Density Evolution Method |
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| Affiliation: | College of Civil Engineering, Tongji University;State Key Laboratory of Disaster Reduction in Civil Engineering(Tongji University), Shanghai 200092, P.R.China |
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| Abstract: | The governing equation and solving algorithm of the probability density evolution method for stochastic dynamical systems were outlined. On this basis, some new advances in the solution of the generalized density evolution equation were discussed, including the ensemble evolution equation and its solution, the rational criterion for partitioning of the probability space, the densification technique of point set and the information reconstruction, etc. |
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