An invariance principle for triangular arrays

被引：5

作者：

D'Aristotile, A ^{[1
]}

机构：

[1] SUNY Coll Plattsburgh, Dept Math, Plattsburgh, NY 12901 USA

来源：

JOURNAL OF THEORETICAL PROBABILITY | 2000年 / 13卷 / 02期

关键词：

triangular array; sign-symmetry; exchangeability; invariance principle; Haar measure;

D O I：

10.1023/A:1007801726073

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

Let A(n,t) be a triangular array of sign-symmetric exchangeable random variables satisfying nE(A(n,i)(2)) --> 1, nE(A(n,i)(4)) --> 0, n(2)E(A(n,1)(2)A(n,2)(2)) --> 1.We show that Sigma(i=1)([nt]) A(ni), 0 less than or equal to t less than or equal to 1, converges to Brownian motion. This is applied to show that if A is chosen from the uniform distribution on the orthogonal group O-n and X-n(t) = Sigma(i=1)([nt]) A(ij), then X-n converges to Brownian motion. Similar results hold For the unitary group.

引用

页码：327 / 341

页数：15

共 17 条

[1] Arratia R., 1990, STAT SCI, P403, DOI [10.1214/ss/1177012015, DOI 10.1214/SS/1177012015]
[2] BHATTACHARYA R, 1990, STOCHASTIC PROCESS A
[3] BILLENSLEY PJ, 1968, CONVERGENCE PROBABIL
[4] Billingsley P., 1986, PROBABILITY MEASURE
[5] Borel E., 1914, Introduction geometrique a quelques theories physiques
[6] BROCKNER T, 1985, REPRESENTATION COMPA
[7] DAFFER P, 1985, LIMIT THEOREM SUMS E
[8] DARISTOTILE A, 1997, BROWNIAN MOTION CLAS
[9] DIACONIS P, 1994, EIGENVALUES RANDOM M, P44
[10] DIACONIS P, 1986, TRACE RANDOM ORTHOGO

← 1 2 →