Probability Surveys

The Skorokhod embedding problem and its offspring

Jan Obłój

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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.

Article information

Source
Probab. Surveys Volume 1 (2004), 321-392.

Dates
First available in Project Euclid: 29 December 2004

Permanent link to this document
https://projecteuclid.org/euclid.ps/1104335302

Digital Object Identifier
doi:10.1214/154957804100000060

Mathematical Reviews number (MathSciNet)
MR2068476

Zentralblatt MATH identifier
1189.60088

Subjects
Primary: 60G40: Stopping times; optimal stopping problems; gambling theory [See also 62L15, 91A60] 60G44: Martingales with continuous parameter 60J25: Continuous-time Markov processes on general state spaces 60J45: Probabilistic potential theory [See also 31Cxx, 31D05]

Keywords
Skorokhod embedding problem Chacon-Walsh embedding Azéma-Yor embedding Root embedding stopping times optimal stopping one-dimensional potential theory

Citation

Obłój, Jan. The Skorokhod embedding problem and its offspring. Probab. Surveys 1 (2004), 321--392. doi:10.1214/154957804100000060. https://projecteuclid.org/euclid.ps/1104335302


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