  The multi-dimensional non-linear Langevin equation with multiplicative
Gaussian white noises in Ito's sense is made covariant with respect to
non-linear transform of variables. The formalism involves no metric or affine
connection, works for systems with or without detailed balance, and is
substantially simpler than previous theories. Its relation with deterministic
theory is clarified. The unitary limit and Hermitian limit of the theory are
examined. Some implications on the choices of stochastic calculus are also
discussed.
