多个区间上平稳序列的最大值及最小值

在条件D(υ_n,u_n),D′ (υ_n,u_n)下,本文将平稳序列的最大值与最小值的渐近独立性推广到有限个不相交区间上,得到定理 {ξ_n}为平稳序列,满足D(υ_n,u_n),D′(υ_n,u_n),u_n=x/a_x+b_x,υ_n=-y/c_n+d_n,a_n>0,c_n>0,J=(α_in,β_in,),i=1,2,…,s,0≤α_1<β_1≤α_2<β_2≤…≤α_n<β_n<∞.如果P(α_n(M_n-b_n)≤x,c_n(M_n-d_n)>-y)→G(x,y)

MAXIMA AND MINIMA OF STATIONARY SEQUENCES ON SEVERAL INTERVALS

Under Conditions D(v,, a.). D1 (u., u.) , the asymptotic independence of maxima and minima of stationary sequences is extended On finite disjoint intervals.Theorem Let {} be a stationary Sequence, satisfying D(v, a,). D1 (v,, u,) , are nondegenerate distributions, then- 6.) < i, c.Cwi^) - d.) >- y}) -i-iandG(z, y) = G(oo, jr)G(z, oo), Where M, = max(^,, - , ?), rn. = min(|, - , |,), {|.} is the independent sequence associated with {?}