Continuity of Zero-Hitting Times of Bessel Processes and Welding Homeomorphisms of SLEK.

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(κ) welding homeomorphism is continuous in κ for κ∈[0,4]. Our motivation behind this is to study the well known problem of the continuity of SLEκ in κ. The main tool in our proofs is random walks with increments distributed as infinite mean Inverse-Gamma laws. [ABSTRACT FROM AUTHOR]