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

摘要

The main result of the article reads: the distribution of a continuousstarting from zero local martingale whose quadratic characteristic is almostsurely absolutely continuous with respect to some non-random increasingcontinuous function is determined by the distribution of the quadraticcharacteristic. Functional limit theorem based on this characterization areproved.