非线性随机参数模型的Legendre多项式逼近误差

利用均方误差最小原则研究参数取值对Legendre多项式逼近误差的影响.分析数值解的均方误差,结果表明,模型参数的选取对近似逼近精度有显著影响,其中参数的标准差σ对近似逼近的精度影响最大,σ增大10倍时,近似逼近的均方误差可能会增加104倍.通过选取合适的参数Legendre多项式能有效逼近含有界随机参数的非线性经济周期模型.

Study on approximation error of a nonlinear business cycle model with bounded random parameters

Based on the principle of minimum mean square error,the influence of parameters selection on the approximation error of Legendre polynomial approximation method is investigated.Analyzing the mean-square error of numerical solution,the results show that the selections of model parameters have great influence on approximate accuracy,and the standard deviation of parameter σ has the greatest influence on accuracy of approximation approach,when σ increased 10 times,the mean square error of approximation approach is likely to increase 104 times.By selecting suitable parameters,the Legendre polynomial approximation is an effective approach in equivalent approximation of a nonlinear business cycle model with bounded random parameters.