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Mathematics > Probability

arXiv:1812.01058 (math)
[Submitted on 3 Dec 2018 (v1), last revised 28 Jul 2021 (this version, v2)]

Title:Propagation of Chaos for reflecting diffusions with local-time dependent noise

Authors:Clayton Barnes
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Abstract:We prove existence and uniqueness of a reaction-diffusion equation whose diffusivity is a non-linear functional of the boundary temperature. We do this by studying systems of one-dimensional reflecting diffusions whose noise is a function of the reflection local-time of the system, and by characterizing the large-scale (hydrodynamic) behavior by showing propagation of chaos. In addition, we analyze the one-particle case by computing the distribution of the hitting times of its reflection local-time. This work is the noise analog of work done by Frank Knight (2001).
Comments: 34 pages
Subjects: Probability (math.PR)
MSC classes: 60
Cite as: arXiv:1812.01058 [math.PR]
  (or arXiv:1812.01058v2 [math.PR] for this version)
  https://doi.org/10.48550/arXiv.1812.01058

Submission history

From: Clayton Barnes [view email]
[v1] Mon, 3 Dec 2018 19:58:59 UTC (19 KB)
[v2] Wed, 28 Jul 2021 01:09:55 UTC (33 KB)
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