Remarks on Gross' technique for obtaining a conformal Skorohod embedding of planar Brownian motion

2019/07/15 by Maher Boudabra, Boudabra, Maher, Greg Markowsky +1 · 3 citations
Economics, Econometrics and Finance · Mathematics · #Complex Variables (math.CV) #FOS: Mathematics #Mathematical Dynamics and Fractals #Probability (math.PR) #Stochastic processes and financial applications #Stochastic processes and statistical mechanics #math.CV #math.PR

paper · pdf · doi:10.48550/arxiv.1907.06335

openalex publication_date 2019/07/15 · arxiv created 2019/12/15 · arxiv updated 2019/12/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04

Abstract

In a recent work by Gross, it was proved that, given a distribution μ with zero mean and finite second moment, we can find a simply connected domain Ω such that if Z_t is a standard planar BM, then Re(Z_τΩ) has the distribution μ. In this note, we extend his method to prove that if μ has a finite L^p moment then the exit time τ_Ω has a finite moment of order (p)/(2).

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