A finite difference scheme for conservation laws driven by Levy noise

摘要

In this paper, we analyse a semidiscrete finite difference scheme for a conservation law driven by a homogeneous multiplicative Levy noise. Thanks to BV estimates, we give a result of compactness for the sequence of approximate solutions generated by the finite difference scheme, and we prove that it converges to the unique entropy solution of the underlying problem as the spatial mesh size Delta x bar right arrow 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(root Delta x).