Dynamic random networks and their graph limits

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Abstract

We study a broad class of stochastic process models for dynamic networks that satisfy the minimal regularity conditions of (i) exchangeability and (ii) càdlàg sample paths. Our main theorems characterize these processes through their induced behavior in the space of graph limits. Under the assumption of time-homogeneous Markovian dependence, we classify the discontinuities of these processes into three types, prove bounded variation of the sample paths in graph limit space and express the process as a mixture of time-inhomogeneous, exchangeable Markov processes with càdlàg sample paths.

Original languageEnglish (US)
Pages (from-to)691-721
Number of pages31
JournalAnnals of Applied Probability
Volume26
Issue number2
DOIs
StatePublished - Apr 2016

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

Keywords

  • Aldous-hoover theorem
  • Combinatorial stochastic process
  • Complex network
  • Dynamic network
  • Exchangeable random graph
  • Graph limit
  • Graphon
  • Markov process
  • Partial exchangeability
  • Time-varying network

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