Large deviations for hierarchical systems of interacting jump processes
type: Item
instance of: scholarly article
title: Large deviations for hierarchical systems of interacting jump processes
zbMATH Open document ID: 0901.60053
DOI: 10.1023/A:1021690707556
author: Boualem Djehiche
author: Alexander Schied
published in: Journal of Theoretical Probability
publication date: 1998-11-11T00:00:00Z
review text: The authors study the limiting behaviour of some Markovian systems of jump processes obeying a two-level hierarchy interaction, which in the limit, as the number of subsystems grows to infinity, satisfy a McKean-Vlasov type equation. For the corresponding empirical distribution, a large deviation upper bound is obtained and the associated rate function is shown to admit two representations, a Lagrangian and a nonvariational (integral) one. Moreover, the admissible paths for the weak solution of the McKean-Vlasov equation are proven to obey some strong differentiability properties. Application to a certain epidemic model is also discussed.
reviewed by: Ostap Hryniv
Mathematics Subject Classification ID: 60J75
Mathematics Subject Classification ID: 60K35
Mathematics Subject Classification ID: 60F10
zbMATH DE Number: 1138554
zbMATH Keywords: two-level hierarchical interaction
zbMATH Keywords: McKean-Vlasov limit
zbMATH Keywords: large deviations
zbMATH Keywords: Orlicz space
zbMATH Keywords: measure-valued process
zbMATH Keywords: weak interaction
zbMATH Keywords: epidemic process
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1138554