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View article: Contagious McKean--Vlasov problems with common noise: from smooth to singular feedback through hitting times
Contagious McKean--Vlasov problems with common noise: from smooth to singular feedback through hitting times Open
We consider a family of McKean--Vlasov equations arising as the large particle limit of a system of interacting particles on the positive half-line with common noise and feedback. Such systems are motivated by structural models for systemi…
View article: Implicit and fully discrete approximation of the supercooled Stefan problem in the presence of blow-ups
Implicit and fully discrete approximation of the supercooled Stefan problem in the presence of blow-ups Open
We consider two implicit approximation schemes of the one-dimensional supercooled Stefan problem and prove their convergence, even in the presence of finite time blow-ups. All proofs are based on a probabilistic reformulation recently cons…
View article: Propagation of minimality in the supercooled Stefan problem
Propagation of minimality in the supercooled Stefan problem Open
Supercooled Stefan problems describe the evolution of the boundary between the solid and liquid phases of a substance, where the liquid is assumed to be cooled below its freezing point. Following the methodology of Delarue, Nadtochiy and S…