Random times and multiplicative systems

The present research is motivated by the recent results of Jeanblanc and Song (2011)  and . Our aim is to demonstrate, with the help of multiplicative systems introduced in Meyer (1979) [21], that for any given positive F$\mathbb{F}$-submartingale F$F$ such that _F∞=1$F_{\infty }=1$, there exists a random time τ$\tau$ on some extension of the filtered probability space such that the Azéma submartingale associated with τ$\tau$ coincides with F$F$. Pertinent properties of this construction are studied and it is subsequently extended to the case of several correlated random times with the predetermined univariate conditional distributions.