Propagation of minimality in the supercooled Stefan problem
Propagation of minimality in the supercooled Stefan problem
复制标题
过冷 Stefan 问题中极小值的传播
DOI：
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发表时间：
2020
期刊：
影响因子：
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通讯作者：
Sara Svaluto
中科院分区：
文献类型：
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作者：
Christa Cuchiero;Stefan Rigger;Sara Svaluto
过冷Stefan问题描述了物质的固相和液相之间的边界的演化，其中液体被假定冷却到其凝固点以下。根据Delarue，Nadtochiy和Shkolnikov的方法，我们通过一定的McKean-Vlasov方程构造了单相一维过冷Stefan问题的解，即使在存在爆破的情况下也可以定义全局解。McKean-Vlasov方程的解是通过碰撞时间相互作用的粒子系统的平均场极限，这对系统风险建模很重要。我们的主要贡献是：（i）我们证明了Skorokhod M1-拓扑的一般紧性定理，它适用于可分解为连续部分和单调部分的过程。(ii)我们证明传播的扰动版本的粒子系统的一般初始条件的混沌。(iii)我们证明了一个猜想Delarue，Nadtochiy和Shkolnikov，有关的解决方案的概念，所谓的最小和物理解决方案，表明最小的解决方案的McKean-Vlasov方程是物理的初始条件是可积的。
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 Shkolnikov, we construct solutions to the one-phase one-dimensional supercooled Stefan problem through a certain McKean-Vlasov equation, which allows to define global solutions even in the presence of blow-ups. Solutions to the McKean-Vlasov equation arise as mean-field limits of particle systems interacting through hitting times, which is important for systemic risk modeling. Our main contributions are: (i) we prove a general tightness theorem for the Skorokhod M1-topology which applies to processes that can be decomposed into a continuous and a monotone part. (ii) We prove propagation of chaos for a perturbed version of the particle system for general initial conditions. (iii) We prove a conjecture of Delarue, Nadtochiy and Shkolnikov, relating the solution concepts of so-called minimal and physical solutions, showing that minimal solutions of the McKean-Vlasov equation are physical whenever the initial condition is integrable.
DOI：
10.2140/pmp.2022.3.171
发表时间：
2019-02
期刊：
Probability and Mathematical Physics
影响因子：
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作者：
F. Delarue;S. Nadtochiy;Mykhaylo Shkolnikov
通讯作者：
F. Delarue;S. Nadtochiy;Mykhaylo Shkolnikov
过冷 Stefan 问题中时间步进格式向自由边界的收敛
DOI：
10.1214/22-aap1815
发表时间：
2023
期刊：
The Annals of Applied Probability
影响因子：
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作者：
Kaushansky, Vadim;Reisinger, Christoph;Shkolnikov, Mykhaylo;Song, Zhuo Qun
通讯作者：
Song, Zhuo Qun