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Liouville distorted Brownian motion

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  • Shin, Jiyong

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.

Suggested Citation

  • Shin, Jiyong, 2020. "Liouville distorted Brownian motion," Statistics & Probability Letters, Elsevier, vol. 156(C).
    • Handle: RePEc:eee:stapro:v:156:y:2020:i:c:s0167715219302366
    DOI: 10.1016/j.spl.2019.108590
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