Exit problem of McKean-Vlasov diffusions in convex landscapes
Exit problem of McKean-Vlasov diffusions in convex landscapes
复制标题
凸景观中 McKean-Vlasov 扩散的退出问题
DOI：
10.1214/ejp.v17-1914
复制
发表时间：
2012
影响因子：
1.4
通讯作者：
Julian Tugaut
中科院分区：
文献类型：
--
作者：
Julian Tugaut
分析了非马尔可夫扩散的退出时间和退出位置。更具体地说，我们关注所谓的自我稳定过程。Herrmann，Imkeller和Peithmann（2008年）研究了这个问题，结果与Freidlin和Wentzell的结果相似。我们的目标是通过一种更直观的方法提供相同的结果，而不需要重建Freidlin和Wentzell的证明。我们的论点如下。一方面，我们建立了一个强版本的混沌传播，它允许链接的McKean-Vlasov扩散和平均场系统中的一个粒子的退出时间。另一方面，我们将Freidlin-Wentzell理论应用于相关的平均场系统，这是一个马尔可夫扩散。
The exit time and the exit location of a non-Markovian diffusion is analyzed. More particularly, we focus on the so-called self-stabilizing process. The question has been studied by Herrmann, Imkeller and Peithmann (in 2008) with results similar to those by Freidlin and Wentzell. We aim to provide the same results by a more intuitive approach and without reconstructing the proofs of Freidlin and Wentzell. Our arguments are as follows. In one hand, we establish a strong version of the propagation of chaos which allows to link the exit time of the McKean-Vlasov diffusion and the one of a particle in a mean-field system. In the other hand, we apply the Freidlin-Wentzell theory to the associated mean field system, which is a Markovian diffusion.
大偏差和自稳定扩散的克拉默斯型定律
影响因子：
1.8
作者：
Herrmann;Samuel;Imkeller;Peithmann
通讯作者：
Peithmann