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Spectral representation of one-dimensional Liouville Brownian Motion and Liouville Brownian excursion (1705.01726v1)
Published 4 May 2017 in math.PR
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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