A finite difference scheme for conservation laws driven by Levy noise
Analysis of PDEs
2016-04-28 v1 Numerical Analysis
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 L^1-difference between the approximate solution and the unique entropy solution converges at a rate O(\sqrt{\Dx}).
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Cite
@article{arxiv.1604.07840,
title = {A finite difference scheme for conservation laws driven by Levy noise},
author = {Ujjwal Koley and Ananta K. Majee and Guy Vallet},
journal= {arXiv preprint arXiv:1604.07840},
year = {2016}
}
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38 Pages