  Asymptotic behavior of the one-dimensional Brownian motion in general random
environments has been investigated by many researchers. However, many of the
methods used in the argument are available only for the one-dimensional case.
In this paper the multidimensional case of the problem is considered, and we
obtain some sufficient conditions for recurrence of the multi-dimensional
Brownian motion in random environments. By using the sufficient conditions we
show that the recurrence of the Brownian motion in Gaussian environments under
some conditions on the correlation functions.
