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2024 | OriginalPaper | Buchkapitel

Linear Stochastic Processes on Networks and Low Rank Graph Limits

verfasst von : Alex Dunyak, Peter E. Caines

Erschienen in: Complex Networks & Their Applications XII

Verlag: Springer Nature Switzerland

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Abstract

The modelling of stochastic linear systems in large complex networks is intractable computationally and may be impossible due to data-collection costs or privacy concerns. Graphon theory provides an approach to overcome these issues by providing potentially simple limit objects for infinite sequences of graphs, permitting one to approximate arbitrarily large networks by infinite dimensional operators. Graphon system theory is extended here to stochastic systems by the use of Q-noise, a generalization of Wiener processes in finite dimensional spaces to processes in function spaces. The theory is developed for low rank systems as a special case.

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Titel: Linear Stochastic Processes on Networks and Low Rank Graph Limits
verfasst von: Alex Dunyak
Peter E. Caines
Verlag: Springer Nature Switzerland
Buch: Complex Networks & Their Applications XII
Print ISBN: 978-3-031-53498-0

Electronic ISBN: 978-3-031-53499-7

Copyright-Jahr: 2024
DOI: https://doi.org/10.1007/978-3-031-53499-7_32

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