At the Mercy of the Common Noise: Blow-ups in a Conditional McKean--Vlasov Problem

Sean Ledger; Andreas Sojmark

At the Mercy of the Common Noise: Blow-ups in a Conditional McKean--Vlasov Problem

Sean Ledger, Andreas Sojmark

Research output: Contribution to journal › Article (Academic Journal)

Abstract

We extend a model of feedback and contagion in large mean-field systems by introducing a common source of noise driven by Brownian motion. Although the dynamics in the model are continuous, the feedback effect can lead to jump discontinuities in the solutions --- i.e. 'blow-ups'. We prove existence of solutions to the corresponding conditional McKean--Vlasov equation and we show that the pathwise realisation of the common noise can both trigger and prevent blow-ups.

Original language	English
Number of pages	21
Journal	arXiv
Publication status	E-pub ahead of print - 16 Jul 2018

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https://arxiv.org/abs/1807.05126

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title = "At the Mercy of the Common Noise: Blow-ups in a Conditional McKean--Vlasov Problem",

abstract = "We extend a model of feedback and contagion in large mean-field systems by introducing a common source of noise driven by Brownian motion. Although the dynamics in the model are continuous, the feedback effect can lead to jump discontinuities in the solutions --- i.e. 'blow-ups'. We prove existence of solutions to the corresponding conditional McKean--Vlasov equation and we show that the pathwise realisation of the common noise can both trigger and prevent blow-ups.",

author = "Sean Ledger and Andreas Sojmark",

year = "2018",

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language = "English",

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T1 - At the Mercy of the Common Noise: Blow-ups in a Conditional McKean--Vlasov Problem

AU - Ledger, Sean

AU - Sojmark, Andreas

PY - 2018/7/16

Y1 - 2018/7/16

N2 - We extend a model of feedback and contagion in large mean-field systems by introducing a common source of noise driven by Brownian motion. Although the dynamics in the model are continuous, the feedback effect can lead to jump discontinuities in the solutions --- i.e. 'blow-ups'. We prove existence of solutions to the corresponding conditional McKean--Vlasov equation and we show that the pathwise realisation of the common noise can both trigger and prevent blow-ups.

AB - We extend a model of feedback and contagion in large mean-field systems by introducing a common source of noise driven by Brownian motion. Although the dynamics in the model are continuous, the feedback effect can lead to jump discontinuities in the solutions --- i.e. 'blow-ups'. We prove existence of solutions to the corresponding conditional McKean--Vlasov equation and we show that the pathwise realisation of the common noise can both trigger and prevent blow-ups.

M3 - Article (Academic Journal)

JO - arXiv

JF - arXiv

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