抛物型扩散模型参数识别的正则化方法

经济计量模型参数识别是对观察的经济数据进行分析而得到经济结果的方法。从数学上讲属于反问题,而这类问题大多是不适定的。本文针对一类典型的抛物型扩散模型采用处理不适定问题的Tikhonov正则化方法来求解。即采用先离散化后正则化的策略利用在误差水平已知的情况下具有三阶收敛速率的算法来处理数值微分,并基于一种快速选择正则参数的混合算法计算正则解。同时对待辨识的分布参数线性和非线性依赖于观测数据两种情况分别进行了数值试验。

On the Regularization Method to the Parametric Recognition of a Parabolic-Type Diffusion Model

The parametric recognition of an econometric model is a method that can come to an economic result through an analysis of the observed economic data.From the view of mathematics,it belongs to an inverse problem and this kind of problem is mostly not well-posed.In this paper,the author tried to solve a type of typical parabolic-type diffusion models by adopting Tikhonov’s regularization method that is used to handle the not well-posed problems.That is to adopt the strategy of ’first discretization,then regularization’ and apply the three-order convergence rate to deal with the numerical differentiation under the situation of known error level and work out the regular solution based on a hybrid algorithm of a fast selection of regular parameter.Meanwhile,the author carries out a numerical experimentation to the awaiting identified distribution of parametric linear and non-linear by referring to the two observed data.