Some New Representations in Bivariate Exchangeability.

Abstract

Consider an array X=(X subij, i,j epsilon N) of random variables, and let U=(U sub ij) and V=(V sub ij) be orthogonal transformations, affecting only finitely many coordinates. Say that X is separately rotatable if UXV sub T = over d X for arbitrary U and V and jointly rotatable if this holds with U=V. Restricting U and V to the class of permutations, we get instead the property of separate or joint exchangeability. Processes on R 2sub+, R sub + x0,1 or 0,1 sub 2 are said to be separately or jointly exchangeable, if the arrays of increments over arbitrary square grids have these properties. For some of the above cases, explicit representations have been obtained by Aldous (1981) and Hoover (1979). The aim of this paper is to continue the work of these authors by deriving some new representations, and by solving the associated uniqueness and continuity problems.

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Document Details

Document Type
Technical Report
Publication Date
Jul 01, 1986
Accession Number
ADA177017

Entities

People

  • Olav Kallenberg

Organizations

  • University of North Carolina at Chapel Hill

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Brownian Motion
  • Coefficients
  • Continuity
  • Data Science
  • Grids
  • Information Science
  • North Carolina
  • Notation
  • Probability
  • Random Variables
  • Rotation
  • Statistics
  • Stochastic Processes
  • Tightness
  • Topology
  • Two Dimensional
  • Weak Convergence

Fields of Study

  • Mathematics

Readers

  • Graph Algorithms and Convex Optimization.
  • Mathematical Modeling and Probability Theory.
  • Statistical inference.