Quantum Mechanics and Brownian Motions

From the point of view that the present formulation of quantum mechanics is very close to the theory of Brownian motions, we search for possible origins of the quantum fluctuation within the framework of new quantization schemes, such as stochastic and/or microcanonical quantizations, for increasing additional fictitious time other than the ordinary one. On the same basis we also show that a D-dimensional quantum system is equivalent to a (D+1)-dimensional classical system.