  We deal with the 3D inviscid Leray-{\alpha} model. The well posedness for
this problem is not known; by adding a random perturbation we prove that there
exists a unique (in law) global solution. The random forcing term formally
preserves conservation of energy. The result holds for initial velocity of
finite energy and the solution has finite energy a.s.. These results are easily
extended to the 2D case.

Probability