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Jin, Xiong

Spectral representation of one-dimensional Liouville Brownian motion and Liouville Brownian excursion. (English) Zbl 07871286

J. Fractal Geom. 11, No. 1-2, 85-109 (2024).
This paper is mainly devoted to the spectral representation of time-changed Brownian motion and Brownian excursion. The author applied Krein’s spectral theory of linear diffusions to study spectral representation of one dimensional Liouville Brownian motion (Section 4.2) and one dimensional Liouville Brownian excursion (Section 4.3).
As an application of the spectral representation, various probabilistic asymptotic behaviours of time changed Brownian motion and Brownian excursion are given in Section 5.
Reviewer: Byoung Soo Kim (Seoul)

MSC:

60J65 Brownian motion
60G22 Fractional processes, including fractional Brownian motion
60D05 Geometric probability and stochastic geometry
28A80 Fractals
34K08 Spectral theory of functional-differential operators

Keywords:

Liouville Brownian motion; Liouville Brownian excursion; Krein’s correspondence; spectral theory; generalized linear diffusions
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References:

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