Continuity of Zero-Hitting Times of Bessel Processes and Welding Homeomorphisms of SLE

Dmitry Beliaev, Vlad Margarint, Atul Shekhar

Research output: Contribution to journalArticlepeer-review

Abstract

We consider a family of Bessel Processes that depend on the starting point x and dimension δ, but are driven by the same Brownian motion. Our main result is that almost surely the first time a process hits 0 is jointly continuous in x and δ, provided δ ≤ 0. As an application, we show that the SLE(≤) welding homeomorphism is continuous in ≤ for ≤ 2 [0; 4]. Our motivation behind this is to study the well known problem of the continuity of SLE≤ in ≤. The main tool in our proofs is random walks with increments distributed as infinite mean Inverse-Gamma laws

Original languageEnglish
Pages (from-to)69-79
Number of pages11
JournalAlea (Rio de Janeiro)
Volume18
Issue number1
DOIs
Publication statusPublished - 2020
Externally publishedYes

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