- Doob’s maximal id, multiplicative decompositions and enlargements of filtrations(arXiv)
Writer : A. Nikeghbali, M. Yor
Summary : Within the principle of progressive enlargements of filtrations, the supermartingale Zt=P(g>t∣Ft) related to an trustworthy time g, and its additive (Doob-Meyer) decomposition, play a vital function. On this paper, we suggest an alternate strategy, utilizing a multiplicative illustration for the supermartingale Z_{t}, based mostly on Doob’s maximal id. We thus give new examples of progressive enlargements. Furthermore, we give, in our setting, a proof of the decomposition method for martingales, utilizing preliminary enlargement strategies, and use it to acquire some path decompositions given the utmost or minimal of some processes
