In this talk, I'll give a brief introduction on the study of the Nevanlinna theory (theory of holomorphic curves) using the stochastic calculus, following the works fo B. Davis, T. K. Carne and A. Atsuji etc.. In particular, I will outline the ideas and compare its method with the classical approach, and outline its advantage on studying the maps on the (general) Kahler manifolds (or even the Rieamnnian manifolds).