Time-splitting approximation of the Cauchy problem for a stochastic conservation law

In this paper, we present a time discretization of a first-order hyperbolic equation of nonlinear type set in Rd and perturbed by a multiplicative noise. Using an operator splitting method, we are able to show the existence of an approximate solution. Thanks to recent techniques of well-posedness theory on this kind of stochastic equations, we show the convergence of such an approximate solution towards the unique stochastic entropy solution of the problem, as the time step of the splitting scheme converges to zero.