On White Noise Space and Levy's Brownian Motion on the Circle
Probability
2020-05-26 v2
Abstract
In this article, we show that the Brownian motion on the circle constructed in Levy (1959) is a regular Euclidean Brownian motion on the half-circle with its own mirror image on the other half-circle, and is degenerated in the sense of Minlos (1959). This raises the question of what the white noise is on the circle. We then formally define the white noise space and its associated Brownian bridge.
Cite
@article{arxiv.1911.03374,
title = {On White Noise Space and Levy's Brownian Motion on the Circle},
author = {Chunfeng Huang and Ao Li},
journal= {arXiv preprint arXiv:1911.03374},
year = {2020}
}