  We consider stochastic differential equations driven by Wiener processes. The
vector fields are supposed to satisfy only local Lipschitz conditions. The
Lipschitz constants of the drift vector field, valid on balls of radius $R$,
are supposed to grow not faster than $\log R$, while those of the diffusion
vector fields are supposed to grow not faster than $\sqrt{\log R}.$ We
regularize the stochastic differential equations by associating with them
approximating ordinary differential equations obtained by discretization of the
increments of the Wiener process on small intervals. By showing that the flow
associated with a regularized equation converges uniformly to the solution of
the stochastic differential equation, we simultaneously establish the existence
of a global flow for the stochastic equation under local Lipschitz conditions.
