Spectral representation of one-dimensional Liouville Brownian Motion and Liouville Brownian excursion
Xiong Jin
TL;DR
This paper applies spectral theory to analyze one-dimensional Liouville Brownian Motion and excursions, estimating fractal dimensions of level sets and exploring asymptotic behaviors.
Contribution
It introduces a spectral approach to study Liouville Brownian Motion and excursions, providing new estimates and asymptotic results.
Findings
Estimated fractal dimensions of level sets
Derived probabilistic asymptotic behaviors
Applied spectral theory to Liouville Brownian Motion
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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Taxonomy
TopicsComplex Systems and Time Series Analysis · Stochastic processes and financial applications · Stochastic processes and statistical mechanics