Convergence of complex asymptotic martingale

Convergences of martingale sequences have wide applications in both theory and practice, and the study of covergences of various martingale sequences is an important subject in probabilistic research in recent years. Covergence of general martingale and covergence of asymptotic martingale were presented in related literatures. This article sets up a complex probability space and presents convergence of complex asymptotic martingale.