A unifying class of Skorokhod embeddings: connecting the Azema-Yor and Vallois embeddings

2005/06/02 by Alexander M. G. Cox, A. M. G. Cox, David Hobson +3 · 1 citation
Mathematics · #60G40 #60J60 (Primary) 60G44 #60J65 (Secondary) #Advanced Algebra and Geometry #Artificial intelligence #Class (philosophy) #Combinatorics #Computer science #FOS: Mathematics #Finite Group Theory Research #Geometric and Algebraic Topology #Mathematics #Probability (math.PR) #Pure mathematics #math.PR #msc:60G40 #msc:60G44 #msc:60J60 #msc:60J65

paper · pdf · doi:10.48550/arxiv.math/0506040

published in arXiv (Cornell University) (Cornell University) · 16 pages, 2 figures

arxiv created 2005/06/02 · openalex publication_date 2005/06/02 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

In this paper we consider the Skorokhod embedding problem in Brownian motion. In particular, we give a solution based on the local time at zero of a variably skewed Brownian motion related to the underlying Brownian motion. Special cases of the construction include the Azema-Yor and Vallois embeddings. In turn, the construction has an interpretation in the Chacon-Walsh framework.

Related

• A conformal Skorokhod embedding
• Classes of Skorokhod Embeddings for the Simple Symmetric Random Walk
• An Optimal Skorokhod Embedding for Diffusions
• Optimal Transport and Skorokhod Embedding
• Skorokhod embeddings, minimality and non-centred target distributions