Random times and multiplicative systems

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