一维非线性扩散过程转移密度的高阶近似方法

摘要

To obtain the transition probability density function (PDF) of diffusion processes ,one of the ways is to numerically solve the corresponding Kolmogorov partial differential equations (PDEs) .A fourth order difference scheme is provided to obtain the numerical solution of the Kolmogorov PDEs . Results of numerical tests show that the provided estimation algorithm based on the fourth order difference scheme to be more accurate than that based on Crank‐Nicolson scheme .Meanwhile ,the fourth order difference estimation method is used to estimate the model of the Chinese interbank offer rate data ,the results show that the long term of mean‐reverting value is 0 .02542 and the viscosity coefficient is around 1 .%考虑一种基于偏微分方程（PDE）的方法来近似一维非线性扩散过程的转移密度，该方法首先构造具有四阶精度的差分法数值求解与该利率模型相关联的偏微分方程，进而获得转移密度函数的高阶近似解。数值模拟试验结果表明，所构造的具有四阶精度的差分法比Crank －Nicolson差分法和Euler法具有更高的效率，并考察所构造的四阶差分估计法在中国银行间同业拆借利率的实证分析，实证结果表明，在所考虑的样本区间内，中国利率的长期水平值是0．02542，且中国货币市场利率粘性系数的值接近于1。