Extremes of $\alpha(t)$-Locally stationary Gaussian processes with   non-constant variances
  With motivation from K. D\c{e}bicki and P. Kisowski (2007), in this paper we derive the exact tail asymptotics of $\alpha(t)$-locally stationary Gaussian processes with non-constant variance functions. We show that some certain variance functions lead to qualitatively new results. 
Long Bai
math.PR