Liouville distorted Brownian motion

Jiyong Shin

Statistics & Probability Letters, 2020, vol. 156, issue C

Abstract: The Liouville Brownian motion was introduced in Garban, (2016) as a time changed process (BAt−1)t≥0 of a planar Brownian motion (Bt)t≥0, where (At)t≥0 is the positive continuous additive functional of (Bt)t≥0 in the strict sense with respect to the Liouville measure. We first consider a distorted Brownian motion (Xt)t≥0 starting from all points in R2 associated to a Dirichlet form (E,D(E)) studied by J. Shin and G. Trutnau [J. Evol. Equ. 17 (2017), no. 3, 931–952]. We show that the positive continuous additive functional (Ft)t≥0 of (Xt)t≥0 in the strict sense with respect to the Liouville distorted measure can be constructed.

Keywords: Dirichlet forms; Distorted Brownian motion; Gaussian free field; Liouville Brownian motion; Revuz correspondence (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1016/j.spl.2019.108590

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