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Numerical stability analysis of the Euler scheme for BSDEs

Abstract : In this paper, we study the qualitative behaviour of approximation schemes for Backward Stochastic Differential Equations (BSDEs) by introducing a new notion of numerical stability. For the Euler scheme, we provide sufficient conditions in the one-dimensional and multidimensional case to guarantee the numerical stability. We then perform a classical Von Neumann stability analysis in the case of a linear driver $f$ and exhibit necessary conditions to get stability in this case. Finally, we illustrate our results with numerical applications.
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Submitted on : Thursday, July 3, 2014 - 2:38:35 PM
Last modification on : Thursday, October 10, 2019 - 2:56:12 PM
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Jean-François Chassagneux, Adrien Richou. Numerical stability analysis of the Euler scheme for BSDEs. SIAM Journal on Numerical Analysis, Society for Industrial and Applied Mathematics, 2015, 53 (2), pp.1172--1193. ⟨10.1137/140977047⟩. ⟨hal-01017969⟩

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