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随机微分方程数值解在泄洪风险分析中的应用
引用本文:徐敏,胡良剑,丁永生,胡盈,周林峰.随机微分方程数值解在泄洪风险分析中的应用[J].数学的实践与认识,2006,36(9):153-157.
作者姓名:徐敏  胡良剑  丁永生  胡盈  周林峰
作者单位:1. 东华大学旭日工商管理学院,上海,200051
2. 东华大学应用数学系,上海,201620
3. 东华大学信息科学与技术学院,上海,201620
基金项目:国家自然科学基金;教育部跨世纪优秀人才培养计划
摘    要:根据泄洪过程中库水位过程的随机微分方程,利用数值解方法,模拟了随机干扰下的库水位及其波动状况.采用相应公式计算了洪水漫越坝顶事件的概率以及库水位过程在不同时刻的样本均值.并通过比较在同样强度的随机干扰下库水位的高低状况,确定出各种泄洪方案的优劣,从而对防洪工作具有重要的指导意义.

关 键 词:随机微分方程  数值解  欧拉法  泄洪风险
修稿时间:2005年6月27日

Numerical Solution of Stochastic Differential Equations with Application to Risk Analysis of Releasing Floodwater
XU Min,HU Liang-jian,DING Yong-sheng,HU Ying,ZHOU Lin-feng.Numerical Solution of Stochastic Differential Equations with Application to Risk Analysis of Releasing Floodwater[J].Mathematics in Practice and Theory,2006,36(9):153-157.
Authors:XU Min  HU Liang-jian  DING Yong-sheng  HU Ying  ZHOU Lin-feng
Abstract:Based on the process of the water level of a reservoir satisfying stochastic differential equations during the process of releasing floodwater,this paper simulates the water level and its fluctuation under stochastic disturbance of Wiener Process by means of numerical solution of stochastic differential equations.It also calculates the mean value at different time of the process of water level as well as the probability of overflowing with corresponding formula.Furthermore,it compares the water level under stochastic disturbance with the same strength in order to ascertain which one is more effective.As a result,it is helpful for the flood practice.
Keywords:stochastic differential equation  numerical solution  Euler method  risk of releasing floodwater
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