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At the mercy of the common noise: blow-ups in a conditional McKean–Vlasov Problem

Ledger, Sean and Søjmark, Andreas ORCID: 0000-0001-7488-0221 (2021) At the mercy of the common noise: blow-ups in a conditional McKean–Vlasov Problem. Electronic Journal of Probability, 26 (none). ISSN 1083-6489

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Identification Number: 10.1214/21-EJP597

Abstract

We extend a model of positive feedback and contagion in large mean-field systems, by introducing a common source of noise driven by Brownian motion. Although the driving dynamics are continuous, the positive feedback effect can lead to ‘blow-up’ phenomena whereby solutions develop jump-discontinuities. Our main results are twofold and concern the conditional McKean–Vlasov formulation of the model. First and foremost, we show that there are global solutions to this McKean–Vlasov problem, which can be realised as limit points of a motivating particle system with common noise. Furthermore, we derive results on the occurrence of blow-ups, thereby showing how these events can be triggered or prevented by the pathwise realisations of the common noise.

Item Type: Article
Additional Information: © 2024 The Author(s)
Divisions: LSE
Subjects: H Social Sciences > HA Statistics
Date Deposited: 05 Jun 2024 12:00
Last Modified: 18 Jul 2024 05:21
URI: http://eprints.lse.ac.uk/id/eprint/123787

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