The Skorokhod embedding problem and its offspring

Details The Skorokhod embedding problem and its offspring The Skorokhod embedding problem and its offspring

2004-01-12

arxiv.org/abs/math/0401114v4

Probability Surveys 2004, Vol. 1, 321-392

Mathematics

Probability

Published at http://dx.doi.org/10.1214/154957804100000060 in the Probability Surveys (http://www.i-journals.org/ps/) by the In

Scientific paper

10.1214/154957804100000060

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. Az\'ema and Yor's and Root's solutions are studied extensively. A possible use of the latter is suggested together with a conjecture.

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