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Max-linear models in random environment

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  • Klüppelberg, Claudia
  • Sönmez, Ercan

Abstract

We extend previous work of max-linear models on finite directed acyclic graphs to infinite graphs as well as random graphs, and investigate their relations to classical percolation theory, more particularly the impact of Bernoulli bond percolation on such models. We show that the critical probability of percolation on the oriented square lattice graph Z2 describes a phase transition in the obtained model. Focus is on the dependence introduced by this graph into the max-linear model. We discuss natural applications in communication networks, in particular, concerning the propagation of influences.

Suggested Citation

  • Klüppelberg, Claudia & Sönmez, Ercan, 2022. "Max-linear models in random environment," Journal of Multivariate Analysis, Elsevier, vol. 190(C).
    • Handle: RePEc:eee:jmvana:v:190:y:2022:i:c:s0047259x22000331
    DOI: 10.1016/j.jmva.2022.104999
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    References listed on IDEAS

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    1. Gissibl, Nadine & Klüppelberg, Claudia & Otto, Moritz, 2018. "Tail dependence of recursive max-linear models with regularly varying noise variables," Econometrics and Statistics, Elsevier, vol. 6(C), pages 149-167.
    2. Nadine Gissibl & Claudia Klüppelberg & Steffen Lauritzen, 2021. "Identifiability and estimation of recursive max‐linear models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 48(1), pages 188-211, March.
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