摘要
对于一个含有未知参数的It(?)随机微分方程中,针对某一实际问题,如果该方程解的值可以量测得到,则可以依据这些量测值,反求方程的未知参数.这就是本文考虑的It(?)随机微分方程之反问题.本文将其转化成一个优化问题,首先研究了It(?)方程的解关于参数的连续依赖性及可微性,进而计算出优化目标泛函关于参数的梯度,最后使用拟牛顿信赖域法来确定未知参数的最佳近似值.
Considering an ItO stochastic differential equation with the unknown parameters, if the solution of the equation could be measured in some actual situations, then the unknown parameters could be computed based on the measured value, it is known as the inverse problem of ItO stochastic differential equation. In this paper, the inverse problem is converted into a optimization problem At first, the continuous dependence and differe- niability of solution of equation upon the parameters are discussed, and then, the gradient of the objective function upon the parameters is worked out,at last, the best approximate values of parameters are obtained by the methods of Quasi-Newton Trust Region.
出处
《应用数学学报》
CSCD
北大核心
2008年第2期314-323,共10页
Acta Mathematicae Applicatae Sinica
基金
国家863基金(2006AA12A113)
中国民航大学基金(04-CAUC-20s)
天津市自然科学基金(06YFJMJC12500)资助项目．
关键词
ItO^随机微分方程
拟牛顿信赖域法
目标泛函对参数的梯度
ItO stochastic differential equation
quasi-Newton trust region method
gradient of a objective functional with repect to the parameters.
