Doob's maximal identity, multiplicative decompositions and enlargements of filtrations

Ashkan Nikeghbali, Marc Yor
2006 Illinois Journal of Mathematics  
2006). Doob's maximal identity, multiplicative decompositions and enlargements of filtrations. Illinois J. Math., 50(1-4):791-814 (electronic). Abstract. In the theory of progressive enlargements of filtrations, the supermartingale Zt = P (g > t | Ft) associated with an honest time g, and its additive (Doob-Meyer) decomposition, play an essential role. In this paper, we propose an alternative approach, using a multiplicative representation for the supermartingale Zt, based on Doob's maximal
more » ... Doob's maximal identity. We thus give new examples of progressive enlargements. Moreover, we give, in our setting, a proof of the decomposition formula for martingales , using initial enlargement techniques, and use it to obtain some path decompositions given the maximum or minimum of some processes.
doi:10.1215/ijm/1258059492 fatcat:s5ibg43tyjfshjl2krpwu2753e