  By reversing the time variable we derive a stochastic representation for
backward incompressible Navier-Stokes equations in terms of stochastic
Lagrangian paths, which is similar to Constantin and Iyer's forward
formulations in \cite{Co-Iy}. Using this representation, a self-contained proof
of local existence of solutions in Sobolev spaces are provided for
incompressible Navier-Stokes equations in the whole space. In two dimensions or
large viscosity, an alternative proof to the global existence is also given.
Moreover, a large deviation estimate for stochastic particle trajectories is
presented when the viscosity tends to zero.
