A finite difference scheme for conservation laws driven by Levy noise

In this paper, we analyze a semi-discrete finite difference scheme for a conservation laws driven by a homogeneous multiplicative Levy noise. Thanks to BV estimates, we show a compact sequence of approximate solutions, generated by the finite difference scheme, converges to the unique entropy solution of the underlying problem, as the spatial mesh size \Dx-->0. Moreover, we show that the expected value of the L^1-difference between the approximate solution and the unique entropy solution converges at a rate O(\sqrt{\Dx}).