  This paper discusses the initial-boundary value problem (with a
nonhomogeneous boundary condition) for a multi-dimensional scalar first-order
conservation law with a multiplicative noise. One introduces a notion of
kinetic formulations in which the kinetic defect measures on the boundary of a
domain are truncated. In such a kinetic formulation one obtains a result of
uniqueness and existence. The unique solution is the limit of the solution of
the stochastic parabolic approximation.
