Graphon-valued processes with vertex-level fluctuations

Stochastic Processes and their Applications, vol. 198, pp. 104961

Abstract

We consider a class of graph-valued stochastic processes in which each vertex has a type that fluctuates randomly over time. Collectively, the paths of the vertex types up to a given time determine the probabilities that the edges are active or inactive at that time. We derive both sample-path large deviation principles and convergence of stochastic processes in the space of graphons as the number of vertices tends to infinity. We demonstrate the flexibility of our framework through several examples.

Authors 3

1. Peter Braunsteins corresponding

   UNSW Sydney

   Affiliation as printed

   School of Mathematics and Statistics, UNSW Sydney, Kensington, 2052, NSW, Australia

2. Frank den Hollander
3. Michel Mandjes Aachen Mathematisch Instituut

   Leiden University · University of Amsterdam

   Affiliation as printed

   Korteweg-de Vries Instituut, Universiteit van Amsterdam, PO Box 94248, Amsterdam, 1090, GE, the Netherlands

   Mathematisch Instituut, Universiteit Leiden, PO Box 9512, Leiden, 2300, RA, the Netherlands