Convergence of local supermartingales and Novikov-Kazamaki type   conditions for processes with jumps
  We characterize the event of convergence of a local supermartingale. Conditions are given in terms of its predictable characteristics and quadratic variation. The notion of extended local integrability plays a key role. We then apply these characterizations to provide a novel proof for the sufficiency and necessity of Novikov-Kazamaki type conditions for the martingale property of nonnegative local martingales with jumps. 
Martin Larsson and Johannes Ruf
math.PR