An Invariance Principle for Triangular Arrays

Anthony D'Aristotile
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Anthony D'Aristotile: SUNY at Plattsburgh

Journal of Theoretical Probability, 2000, vol. 13, issue 2, 327-341

Abstract: Abstract Let A n, i be a triangular array of sign-symmetric exchangeable random variables satisfying nE(A 2 n, i )→1, nE(A 4 n, i )→0, n 2 E(A 2 n, 1 A 2 n, 2)→1. We show that ∑[nt] i=1 A ni, 0≤t≤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)=∑[nt] i=1 A ii, then X n converges to Brownian motion. Similar results hold for the unitary group.

Keywords: triangular array; sign-symmetry; exchangeability; invariance principle; Haar measure (search for similar items in EconPapers)
Date: 2000
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DOI: 10.1023/A:1007801726073

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