通过弹性停止时间的正反馈McKean-Vlasov方程

IF 0.5 4区数学 Q4 STATISTICS & PROBABILITY

Electronic Communications in Probability Pub Date : 2022-01-01 DOI:10.1214/22-ecp482

B. Hambly, Julian Meier

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引用次数: 2

摘要

通过弹性停止时间证明了具有正反馈的McKean-Vlasov方程的物理解和最小解的存在唯一性。我们通过建立这个问题和一个有吸收停止时间的问题之间的关系来做到这一点。我们向McKean-Vlasov方程展示了粒子系统的收敛性。此外，我们还建立了弹性McKean-Vlasov问题在弹性参数趋近于无穷大或趋近于零时对吸收停止时间问题和对反射布朗运动问题的收敛性。

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McKean-Vlasov equations with positive feedback through elastic stopping times

We prove existence and uniqueness of physical and minimal solutions to McKean-Vlasov equations with positive feedback through elastic stopping times. We do this by establishing a relationship between this problem and a problem with absorbing stopping times. We show convergence of a particle system to the McKean-Vlasov equation. Moreover, we establish convergence of the elastic McKean-Vlasov problem to the problem with absorbing stopping times and to a reﬂecting Brownian motion as the elastic parameter goes to inﬁnity or zero respectively.

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来源期刊

Electronic Communications in Probability 工程技术-统计学与概率论

CiteScore

1.00

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： The Electronic Communications in Probability (ECP) publishes short research articles in probability theory. Its sister journal, the Electronic Journal of Probability (EJP), publishes full-length articles in probability theory. Short papers, those less than 12 pages, should be submitted to ECP first. EJP and ECP share the same editorial board, but with different Editors in Chief.