  WE PRESENT THE RANDOM REPRESENTATIONS FOR THE NAVIER-STOKES VORTICITY
EQUATIONS FOR AN INCOMPRESSIBLE FLUID IN A SMOOTH MANIFOLD WITH BOUNDARY AND
REFLECTING BOUNDARY CONDITIONS FOR THE VORTICITY. WE SPECIALIZE OUR
CONSTRUCTIONS TO R(n-1)xR+. WE EXTEND THESE CONSTRUCTIONS TO GIVE THE RANDOM
REPRESENTATIONS FOR THE KINEMATIC DYNAMO PROBLEM OF MAGNETOHYDRODYNAMICS. WE
CARRY OUT THESE INTEGRATIONS THROUGH THE APPLICATION OF THE METHODS OF
STOCHASTIC DIFFERENTIAL GEOMETRY, I.E. THE GAUGE THEORY OF DIFFUSION PROCESSES
ON SMOOTH MANIFOLDS.
