A Characterization Theorem for the Distribution of a Continuous Local Martingale and Related Limit Theorems

Abstract

The main result of the article reads: the distribution of a continuous starting from zero local martingale whose quadratic characteristic is almost surely absolutely continuous with respect to some non-random increasing continuous function is determined by the distribution of the quadratic characteristic. Functional limit theorem based on this characterization are proved.

This paper has been withdrawn by the author, because the characterization theorem is incorrect (though the author results sustain with minor changes)