Random times and multiplicative systems

The present research is motivated by the recent results of Jeanblanc and Song (2011) [10] and [11]. Our aim is to demonstrate, with the help of multiplicative systems introduced in Meyer (1979) [21], that for any given positive FF-submartingale FF such that F∞=1F∞=1, there exists a random time ττ on some extension of the filtered probability space such that the Azéma submartingale associated with ττ coincides with FF. 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.