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On White Noise Space and Levy's Brownian Motion on the Circle

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.

preprint2020arXivOpen access
Chunfeng HuangAo Li
math.PR
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Chunfeng HuangAo Li

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