Itô-Wiener expansion for functionals of the Arratia's flow n-point motion

The structure of square integrable functionals measurable with respect to the $n$-point motion of the Arratia flow is studied. Relying on the change of measure technique, a new construction of multiple stochastic integrals along trajectories of the flow is presented. The analogue of the Itô-Wiener expansion for square integrable functionals from the Arratia's flow $n$-point motion is constructed.