The invariance principle for linear processes generated by a negatively associated sequence and its applications (Q1879151)

Let \((\varepsilon_n,\,n\in\mathbb{Z})\) be a strongly stationary, negatively associated sequence of centered random variables with finite variance. Define \(X_t= \sum^\infty_{j=0} a_j\varepsilon_{t- j}\), where \(\sum^\infty_{j=0} |a_j|<\infty\), and \(S_n= \sum^n_{t=1} X_t\), \(n\geq 1\). The author establishes the weak invariance principle for processes \(Y_n(t)= (1/\sqrt{n})S_{[nt]}\), \(t\in [0, 1]\), \(n\geq 1\).