一类非线性随机微分方程的参数估计

摘要

利用极大似然估计方法,考虑一类具有小扰动的非线性随机微分方程的参数估计问题.讨论小扰动项ε→0或时间T→∞时估计量的性质,证明了:当ε→0时,未知参数的估计量具有无偏性及渐近一致性;当ε取固定值和ε→0时,分别给出了估计量^αε在T→∞时的渐近分布.最后给出数值模拟结果,验证了估计量的无偏性及其渐近正态性.%By using the maximum likelihood estimation (MLE)method,we considered the parameter estimation problem of a class of nonlinear stochastic differential equations with small perturbation. We discussed the properties of the esitmator as the small perturbation parameterε→0 or time T→∞, and proved that the estimator of unknown parameter had unbiasedness and asymptotic consistency asε→0.Whenεtook a fixed value andε→0,we gave the asymptotic distribution of the estimator^αεas T→∞ respectively.Finallay,we gave the numerical simulation results to verify the unbiasedness and asymptotic normality of estimator.