A new proof for the conditions of Novikov and Kazamaki

Abstract

This paper provides a novel proof for the sufficiency of certain well-known criteria that guarantee the martingale property of a continuous, nonnegative local martingale. More precisely, it is shown that generalizations of Novikov's condition and Kazamaki's criterion follow directly from the existence of F\"ollmer's measure. This approach allows to extend well-known criteria of martingality from strictly positive to only nonnegative, continuous local martingales.