@article{ECP2889,
author = {Alexander Cox and Martin Klimmek},
title = {From minimal embeddings to minimal diffusions},
journal = {Electron. Commun. Probab.},
fjournal = {Electronic Communications in Probability},
volume = {19},
year = {2014},
keywords = {diffusion, minimality, local-martingales, Skorokhod embedding problem},
abstract = {We show that there is a one-to-one correspondence between diffusions and the solutions of the Skorokhod Embedding Problem due to Bertoin and Le-Jan. In particular, the minimal embedding corresponds to a "minimal local martingale diffusion", which is a notion we introduce in this article. Minimality is closely related to the martingale property. A diffusion is minimal if it minimises the expected local time at every point among all diffusions with a given distribution at an exponential time. Our approach makes explicit the connection between the boundary behaviour, the martingale property and the local time characteristics of time-homogeneous diffusions.},
pages = {no. 34, 1-13},
issn = {1083-589X},
doi = {10.1214/ECP.v19-2889},
url = {http://ecp.ejpecp.org/article/view/2889}}