一类Gauss序列极值的极限律

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2、22%Gtwy$Vol.27,No.220075ÆJOURNALOFMATHEMATICALRESEARCHANDEXPOSITIONMay,2007X,6:1000-341X(2007)02-0397-06-FBAT=Gauss?7Z07^℄(V8Yx&ss
V8q524000)(E-mail:kmzhling@sina.com)WR:R

3、F"^Gaussr-4XB7+)A
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f(r-ov$48/:cox-X
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4、F"^ovHMSC(2000):60F15;60F05[
2<:O211.41V[1−3]U!℄q,beH!W,uwE:2./B>E!℄q,8l[&#uw{E!℄Gaussq,b3WA6*(H!W,CY3W,A6U;*(ir,j6)%,[nuG1k)%,nuGe'rb,[nuG9{Xn,n≥1}%GaussqiU`Erij=cov(Xi,Xj),3>i

5、≥un≥···≥unrH!+((u(k)xk+b(k=1,2,...,r),x≥x≥···≥x,n=√ann12r(2)a=2logn,b=a−(2a)−1(loglogn+log4π).nnnnCbcox-3W,{n!eh√U>13Ncox-Wa)<τ(ζ)=exp(−x−γ+2γζ),&"ζ%∗∗ÆNN;_*(,3W_1−p,3WN0cox-Wa)

6、rrP{N∗(B)=k}=...P{N∗(B)=k

7、N(B)=s}·P{N(B)=s}iiiiiiiii=1s1=k1sr=kri=1i=1i=1G3ED:2004-06-28;9HED:2005-08-14398Fsvx#27

8、∞"r#ZrXYs+∞Y(m(B)τ(z))si=ipki(1−p)si−ki·ie−m(Bi)τ(z)ϕ(z)dzki−∞si!si=kii=1i=1i=1,2,...,rZ+∞r"∞s#YXs(m(B)τ(z))i=ipki(1−p)si−kiie−m(Bi)τ(z)ϕ(z)dz−∞kisi!i=1si=kiZ+∞Yr(m(

9、B)·pτ(z))ki=ie−m(Bi)pτ(z)ϕ(z)dz,−∞ki!i=1∗BN)2(Æt)9ξ1,ξ2,...,ξneη1,η2,...,ηn}X%aÆEξiξj=Λ1,Eηη=Λ0,ω=max(

10、Λ1

11、,

12、Λ0

13、),i,j=1,2,...,n;u,u,...,uijijijijijij12nX=Eu=min(

14、u1

15、,

16、u2

17、,...,

18、un

19、),

20、P{ξj≤uj,j=1,2,...,n}−P{ηj≤uj,j=1,2,...,n}

21、Xu210≤K

22、Λij−Λij

23、exp−.1+ωij1≤i

24、l[e[4]"81–83zU>39{Xn,n≥1}%GaussqiU`Erij=cov(Xi,Xj)(sup(

25、rij

26、,i6=γ,u=x+b(x∈R),j)<1,+(1)>9ρn=lognnann&"an,bn[(2)>(i)rij→0(j−i−→+∞);Pu2(ii)

27、r−ρ

28、exp−n→0(n→∞),1≤i

29、rij

30、,ρn).l[e[5]"2.2S:5j(1)(2)(r)Yn(Yn(n)=Xj)>rH!un≥un≥···≥un,W,CY3WNn.(k)(k)(

31、k)Yn>un,WR{Y3WNn,SpNn?!T6hLk6(k=1,2,...,r)._aDD>RCY3WN,p3WNn}GA3WN.√9ζ%Æ{σ1j

32、j=1,2,...}hLr6)

33、ζ=z}=τ1(z)/τr(z),s=r,√&