非时齐Markov链泛函的弱收敛

Weak convergence of functionals of non-homogeneous Markov chain

本文考虑了非时齐Markov链泛函的弱收敛定理.本文的极限过程是一类随机积分型的随机过程.作为应用,首先考虑了单位根检验问题;其次考虑了协整回归模型中参数最小二乘估计量的渐近分布.这两类问题中,均涉及了收敛至随机积分的弱收敛定理.

In this paper, we obtain the weak convergence of functionals of non-homogeneous Markov chain. Our limiting processes are stochastic integrals. As applications, we first consider the unit root testing problem, which involves the weak convergence to stochastic integrals. Furthermore, we study the asymptotic distribution of least squares estimator in cointegrating regression model which involves endogeneity, nonstationary and nonlinearity, which depends heavily on weak convergence to stochastic integral.