The Annals of Applied Probability
- Ann. Appl. Probab.
- Volume 26, Number 2 (2016), 691-721.
Dynamic random networks and their graph limits
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.
Ann. Appl. Probab., Volume 26, Number 2 (2016), 691-721.
Received: October 2014
Revised: December 2014
First available in Project Euclid: 22 March 2016
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Time-varying network dynamic network complex network exchangeable random graph partial exchangeability graph limit graphon Markov process Aldous–Hoover theorem combinatorial stochastic process
Crane, Harry. Dynamic random networks and their graph limits. Ann. Appl. Probab. 26 (2016), no. 2, 691--721. doi:10.1214/15-AAP1098. https://projecteuclid.org/euclid.aoap/1458651817