The Annals of Applied Probability

Dynamic random networks and their graph limits

Harry Crane

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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.

Article information

Source
Ann. Appl. Probab., Volume 26, Number 2 (2016), 691-721.

Dates
Received: October 2014
Revised: December 2014
First available in Project Euclid: 22 March 2016

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1458651817

Digital Object Identifier
doi:10.1214/15-AAP1098

Mathematical Reviews number (MathSciNet)
MR3476622

Zentralblatt MATH identifier
1342.60163

Subjects
Primary: 60G05: Foundations of stochastic processes 60G09: Exchangeability 60J25: Continuous-time Markov processes on general state spaces 90B15: Network models, stochastic

Keywords
Time-varying network dynamic network complex network exchangeable random graph partial exchangeability graph limit graphon Markov process Aldous–Hoover theorem combinatorial stochastic process

Citation

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


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