An explicit solution to the Skorokhod embedding problem for functionals of excursions of Markov processes |
| |
Institution: | Laboratoire de Probabilités, Université Paris 6, 4 pl. Jussieu - boîte 188, 75252 Paris Cedex 05, France;Faculty of Mathematics, Warsaw University, Banacha 2, 02-097 Warszawa, Poland |
| |
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 Obłój and Yor J. Obłój, 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 Obłój and Yor J. Obłój, 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: | |
本文献已被 ScienceDirect 等数据库收录! |
|