An explicit solution to the Skorokhod embedding problem for functionals of excursions of Markov processes

Jan Oblój

Stochastic Processes and their Applications, 2007, vol. 117, issue 4, 409-431

Abstract: We develop an explicit non-randomized solution to the Skorokhod embedding problem in an abstract setup of signed functionals of excursions of Markov processes. Our setting allows us to solve the Skorokhod embedding problem, in particular, for the age process of excursions of a Markov process, for diffusions and their signed age processes, for Azéma's martingale and for Bessel processes of dimension smaller than 2. This work is a continuation and an important generalization of Oblój and Yor [J. Oblój, M. Yor, An explicit Skorokhod embedding for the age of Brownian excursions and Azéma martingale, Stochastic Process. Appl. 110 (1) (2004) 83-110]. Our methodology is based on excursion theory and the solution to the Skorokhod embedding problem is described in terms of the Itô measure of the functional. We also derive an embedding for positive functionals and we correct a mistake in the formula of Oblój and Yor [J. Oblój, M. Yor, An explicit Skorokhod embedding for the age of Brownian excursions and Azéma martingale, Stochastic Process. Appl. 110 (1) (2004) 83-110] for measures with atoms.

Keywords: Skorokhod; embedding; problem; Excursion; theory; Functional; of; excursion; Azema-Yor; stopping; time; Vallois; stopping; time; Azema; martingale; Age; process; Bessel; process; Cox-Ingersoll-Ross; process (search for similar items in EconPapers)
Date: 2007
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0304-4149(06)00122-0
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:117:y:2007:i:4:p:409-431

Ordering information: This journal article can be ordered from
http://http://www.elsevier.com/wps/find/supportfaq.cws_home/regional
https://shop.elsevie ... _01_ooc_1&version=01

Access Statistics for this article

Stochastic Processes and their Applications is currently edited by T. Mikosch

More articles in Stochastic Processes and their Applications from Elsevier
Bibliographic data for series maintained by Catherine Liu ().