A finite difference scheme for conservation laws driven by Levy noise

2016/04/26 by Koley, Ujjwal, Majee, Ananta K., Vallet, Guy
#Analysis of PDEs (math.AP) #FOS: Mathematics #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.1604.07840

Abstract

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 L¹-difference between the approximate solution and the unique entropy solution converges at a rate O(√(\Dx)).

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