Reducing exit-times of diffusions with repulsive interactions

IF 0.6 4区 数学 Q4 STATISTICS & PROBABILITY Esaim-Probability and Statistics Pub Date : 2021-10-25 DOI:10.1051/ps/2023012
P. C. D. Raynal, M. H. Duong, Pierre Monmarch'e, Milica Tomavsevi'c, J. Tugaut
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引用次数: 4

Abstract

In this work we prove a Kramers’ type law for the low-temperature behavior of the exittimes from a metastable state for a class of self-interacting nonlinear diffusion processes. Contrary to previous works, the interaction is not assumed to be convex, which means that this result covers cases where the exit-time for the interacting process is smaller than the exittime for the associated non-interacting process. The technique of the proof is based on the fact that, under an appropriate contraction condition, the interacting process is conveniently coupled with a non-interacting (linear) Markov process where the interacting law is replaced by a constant Dirac mass at the fixed point of the deterministic zero-temperature process.
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减少具有排斥相互作用的扩散的退出时间
本文证明了一类自相互作用非线性扩散过程从亚稳态出发的低温行为的Kramers型定律。与以前的工作相反,交互作用不被假设为凸的,这意味着这个结果涵盖了交互过程的退出时间小于相关非交互过程的退出时间的情况。证明的技术是基于这样一个事实,即在适当的收缩条件下,相互作用过程可以方便地与非相互作用(线性)马尔可夫过程耦合,其中相互作用定律在确定性零温度过程的固定点被恒定的狄拉克质量所取代。
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来源期刊
Esaim-Probability and Statistics
Esaim-Probability and Statistics STATISTICS & PROBABILITY-
CiteScore
1.00
自引率
0.00%
发文量
14
审稿时长
>12 weeks
期刊介绍: The journal publishes original research and survey papers in the area of Probability and Statistics. It covers theoretical and practical aspects, in any field of these domains. Of particular interest are methodological developments with application in other scientific areas, for example Biology and Genetics, Information Theory, Finance, Bioinformatics, Random structures and Random graphs, Econometrics, Physics. Long papers are very welcome. Indeed, we intend to develop the journal in the direction of applications and to open it to various fields where random mathematical modelling is important. In particular we will call (survey) papers in these areas, in order to make the random community aware of important problems of both theoretical and practical interest. We all know that many recent fascinating developments in Probability and Statistics are coming from "the outside" and we think that ESAIM: P&S should be a good entry point for such exchanges. Of course this does not mean that the journal will be only devoted to practical aspects.
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