Spreading and Predictable Sampling for Exchangeable Sequences and Processes.

Abstract

Rydll-Nardzewski (1957) proved that an infinite sequence of random variables is exchangeable, if every subsequence has the same distribution. This document discusses some restatements and extensions of this result in terms of martingales and stopping times. In the other direction, it is shown that the distribution of a finite or infinite exchangeable sequence is invariant under sampling by means of a.s. distinct (but not necessarily ordered) predictable stopping times. Both types of result generalize to exchangeable processes in continuous time. (Author)

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Document Details

Document Type
Technical Report
Publication Date
May 01, 1986
Accession Number
ADA172003

Entities

People

  • Olav Kallenberg

Organizations

  • University of North Carolina at Chapel Hill

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Analogs
  • Brownian Motion
  • Continuity
  • Convergence
  • Differential Equations
  • Integrals
  • Intervals
  • Invariance
  • Mathematics
  • North Carolina
  • Permutations
  • Probability
  • Random Variables
  • Sequences
  • Standards
  • Statistics
  • Stochastic Processes

Fields of Study

  • Mathematics

Readers

  • Mathematical Modeling and Probability Theory.