@article{ECP2310,
author = {Umut Çetin},
title = {Filtered Azéma martingales},
journal = {Electron. Commun. Probab.},
fjournal = {Electronic Communications in Probability},
volume = {17},
year = {2012},
keywords = {Azéma's martingale; excursions of Brownian motion; skew Brownian motion; optional projection; local times},
abstract = {We study the optional projection of a standard Brownian motion on the natural filtration of certain kinds of observation processes. The observation process, $Y$, is defined as a solution of a stochastic differential equation such that it reveals some (possibly noisy) information about the signs of the Brownian motion when $Y$ hits $0$. As such, the associated optional projections are related to Azéma's martingales which are obtained by projecting the Brownian motion onto the filtration generated by observing its signs.
},
pages = {no. 62, 1-13},
issn = {1083-589X},
doi = {10.1214/ECP.v17-2310},
url = {http://ecp.ejpecp.org/article/view/2310}}