Strong convergence rates for backward Euler on a class of nonlinear jump-diffusion problems |
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Authors: | Desmond J. Higham Peter E. Kloeden |
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Affiliation: | 1. Department of Mathematics, University of Strathclyde, Glasgow G1 1XH, UK;2. Fachbereich Mathematik, Johann Wolfgang Goethe-Universität, D-60054 Frankfurt am Main, Germany |
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Abstract: | We generalise the current theory of optimal strong convergence rates for implicit Euler-based methods by allowing for Poisson-driven jumps in a stochastic differential equation (SDE). More precisely, we show that under one-sided Lipschitz and polynomial growth conditions on the drift coefficient and global Lipschitz conditions on the diffusion and jump coefficients, three variants of backward Euler converge with strong order of one half. The analysis exploits a relation between the backward and explicit Euler methods. |
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Keywords: | 65C30 60H10 |
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