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arXiv · 1705.01726

Spectral representation of one-dimensional Liouville Brownian Motion and Liouville Brownian excursion

Xiong Jin
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Abstract

In this paper we apply the spectral theory of linear diffusions to study the one-dimensional Liouville Brownian Motion and Liouville Brownian excursions from a given point. As an application we estimate the fractal dimensions of level sets of one-dimensional Liouville Brownian motion as well as various probabilistic asymptotic behaviours of Liouville Brownian motion and Liouville Brownian excursions.

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Xiong Jin. 2017-05-04. Spectral representation of one-dimensional Liouville Brownian Motion and Liouville Brownian excursion. https://arxiv.org/abs/1705.01726

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