Joint asymptotic distributions of maximas for multi-variate normal process

Ｊｏｉｎｔａｓｙｍｐｔｏｔｉｃｄｉｓｔｒｉｂｕｔｉｏｎｓｏｆｍａｘｉｍａｓｏｆｍｕｌｔｉ－ｖａｒｉａｔｅｎｏｒｍａｌｐｒｏｃｅｓｓＰｅｎｇＺｕｏｘｉａｎｇ（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＳｏｕｔｈｗｅｓｔＣｈｉｎａＮｏｒｍａｌＵｎｉ...

X(t) , t≥ 0} = { (ζ_1 (t) , … , ζ_p(t)) , t ≥ 0} is a p-dimensional normal process, if thecross -covariance functions and covariance functions of p component processes satisfy certain condi-tions, the asymptotic independence of the maxima of the p component normal processes is proved. Asp = 2 , the asymptotic joint distributions of maxima and minima of a non-differentiable stationary nor-mal process are also obtained.