Propagation of Chaos for reflecting diffusions with local-time dependent noise
Probability
2021-07-29 v2
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).
Keywords
Cite
@article{arxiv.1812.01058,
title = {Propagation of Chaos for reflecting diffusions with local-time dependent noise},
author = {Clayton Barnes},
journal= {arXiv preprint arXiv:1812.01058},
year = {2021}
}
Comments
34 pages