  The relationship between the Yang-Mills equations and the stochastic analogue
of Levy differential operators is studied. The value of the stochastic Levy
Laplacian is found by means of Cesaro averaging of directional derivatives on
the stochastic parallel transport. It is shown that the Yang-Mills equations
and the Levy-Laplace equation for such Laplacian are not equivalent as in the
deterministic case. An equation equivalent to the Yang-Mills equations is
obtained. The equation contains the stochastic Levy divergence. It is proved
that the Yang-Mills action functional can be represented as an
infinite-dimensional analogue of the Direchlet functional of chiral field. This
analogue is also derived using Cesaro averaging.
