Journal article
A free boundary characterisation of the Root barrier for Markov processes
- Abstract:
-
We study the existence, optimality, and construction of non-randomised stopping times that solve the Skorokhod embedding problem (SEP) for Markov processes which satisfy a duality assumption. These stopping times are hitting times of space-time subsets, so-called Root barriers. Our main result is, besides the existence and optimality, a potential-theoretic characterisation of this Root barrier as a free boundary. If the generator of the Markov process is sufficiently regular, this reduces to an obstacle PDE that has the Root barrier as free boundary and thereby generalises previous results from one-dimensional diffusions to Markov processes. However, our characterisation always applies and allows, at least in principle, to compute the Root barrier by dynamic programming, even when the well-posedness of the informally associated obstacle PDE is not clear. Finally, we demonstrate the flexibility of our method by replacing time by an additive functional in Root’s construction. Already for multi-dimensional Brownian motion this leads to new class of constructive solutions of (SEP).
- Publication status:
- Published
- Peer review status:
- Peer reviewed
Actions
Access Document
- Files:
-
-
(Preview, Version of record, pdf, 1.9MB, Terms of use)
-
- Publisher copy:
- 10.1007/s00440-021-01052-6
Authors
- Publisher:
- Springer
- Journal:
- Probability Theory and Related Fields More from this journal
- Volume:
- 180
- Issue:
- 1
- Pages:
- 33-69
- Publication date:
- 2021-05-06
- Acceptance date:
- 2021-03-25
- DOI:
- EISSN:
-
1432-2064
- ISSN:
-
0178-8051
- Language:
-
English
- Keywords:
- Pubs id:
-
1023540
- Local pid:
-
pubs:1023540
- Deposit date:
-
2022-12-14
Terms of use
- Copyright holder:
- Gassiat et al.
- Copyright date:
- 2021
- Rights statement:
- © The Author(s) 2021. This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.
- Licence:
- CC Attribution (CC BY)
If you are the owner of this record, you can report an update to it here: Report update to this record