Asymptotics of Maxima of Strongly Dependent Gaussian Processes

Let $\{X_{n}(t), t\in[0,\infty)\}, n\in\mathbb{N}$ be a sequence of centered dependent stationary Gaussian processes. The limit distribution of $\sup_{t\in[0,T(n)]}|X_{n}(t)|$ is established as $r_{n}(t)$, the correlation function of $X_{n}$ satisfies the local and long range strong dependence conditions, which extends the results obtained by Seleznjev (1991).