平稳高斯过程最大值的极限分布

Limiting Distribution for the Maxima of Stationary Gaussian Processes

设{(ξt),t≥0}为平稳高斯过程,E((ξt))=0,E(2ξ(t))=1,E(ξ(0)(ξt))=r(t).当r(t)logt r∈(0,∞),且r(t)单调下降到零时,得到了M(T)=sup{ξ(t);0≤t≤T}的极限分布.

Let {ξ(t),t≥0} be a stationary Gaussian process with E(ξ(t))=0,E(ξ~2(t))=1,E(ξ(0)ξ(t))=r(t).When r(t)logtr∈(0,∞) and r(t) converges to zero monotonely,the limiting distribution of M(T)=sup{ξ(t),t≥0} has been obtained in this paper.