  Stochastic differential equations (SDE) are widely used in modeling
stochastic dynamics in literature. However, SDE alone is not enough to
determine a unique process. A specified interpretation for stochastic
integration is needed. Different interpretations specify different dynamics.
Recently, a new interpretation of SDE is put forward by one of us. This
interpretation has a built-in Boltzmann-Gibbs distribution and shows the
existence of potential function for general processes, which reveals both local
and global dynamics. Despite its powerful property, its relation with classical
ones in arbitrary dimension remains obscure. In this paper, we will clarify
such connection and derive the concise relation between the new interpretation
and Ito process. We point out that the derived relation is experimentally
testable.
