2008/03/14 by Dapeng Zhan, Zhan, Dapeng · 2 citations
Economics, Econometrics and Finance · Mathematics · #60D05 #FOS: Mathematics #Mathematical Dynamics and Fractals #Probability (math.PR) #Stochastic processes and financial applications #Stochastic processes and statistical mechanics #math.PR #msc:60D05
paper · pdf · doi:10.48550/arxiv.0803.2223
30 pages; some changes have been made to Introduction and References
openalex publication_date 2008/03/14 · arxiv created 2008/03/23 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We improve the geometric properties of SLE(κ;ρ) processes derived in an earlier paper, which are then used to obtain more results about the duality of SLE. We find that for κ∈ (4,8), the boundary of a standard chordal SLE(κ) hull stopped on swallowing a fixed x∈\R\sem\0\ is the image of some SLE(16/κ;ρ) trace started from a random point. Using this fact together with a similar proposition in the case that κ≥ 8, we obtain a description of the boundary of a standard chordal SLE(κ) hull for κ>4, at a finite stopping time. Finally, we prove that for κ>4, in many cases, the limit of a chordal or strip SLE(κ;ρ) trace exists.