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At the Mercy of the Common Noise: Blow-ups in a Conditional McKean--Vlasov Problem. (arXiv:1807.05126v1 [math.PR])
来源于:arXiv
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. 查看全文>>