Filtered Az\'ema martingales
  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 Az\'ema's martingales which are obtained by projecting the Brownian motion onto the filtration generated by observing its signs. 
Umut \c{C}etin
math.PR