The Skorokhod embedding problem and its offspring

2004/01/01 by Jan Obłój, Jan Obloj · 3 citations
Mathematics · Physics and Astronomy · #Holomorphic and Operator Theory #Quantum Mechanics and Non-Hermitian Physics #Spectral Theory in Mathematical Physics #math.HO #math.PR #msc:60G40 #msc:60G44 #msc:60J25 #msc:60J45

paper · pdf · doi:10.1214/154957804100000060

published as Probability Surveys 2004, Vol. 1, 321-392 · Published at http://dx.doi.org/10.1214/154957804100000060 in the Probability Surveys (http://www.i-journals.org/ps/) by the Institute of Mathematical Statistics (http://www.imstat.org)

openalex publication_date 2004/01/01 · arxiv created 2005/11/10 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This is a survey about the Skorokhod embedding problem. It presents all known solutions together with their properties and some applications. Some of the solutions are just described, while others are studied in detail and their proofs are presented. A certain unification of proofs, based on one-dimensional potential theory, is made. Some new facts which appeared in a natural way when different solutions were cross-examined, are reported. Azéma and Yor’s and Root’s solutions are studied extensively. A possible use of the latter is suggested together with a conjecture.

Citations

• An approximation of partial sums of independent RV's, and the sample DF. II
• An approximation of partial sums of independent RV'-s, and the sample DF. I

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