On rate of convergence of finite difference scheme for degenerate parabolic-hyperbolic PDE with Levy noise

In this article, we consider a semi discrete finite difference scheme for a degenerate parabolic-hyperbolic PDE driven by Lévy noise in one space dimension. Using bounded variation estimations and a variant of classical Kružkov’s doubling of variable approach, we prove that expected value of the $L^1$-difference between the unique entropy solution and approximate solution converges at a rate of $(\mathrm{\Delta }x{)}^{\frac{1}{7}}$, where $\mathrm{\Delta }x$ is the spatial mesh size.