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BIT Numerical Mathematics

Erschienen in:

09.07.2016

Mean-square convergence of the BDF2-Maruyama and backward Euler schemes for SDE satisfying a global monotonicity condition

verfasst von: Adam Andersson, Raphael Kruse

Erschienen in: BIT Numerical Mathematics | Ausgabe 1/2017

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Abstract

In this paper the numerical approximation of stochastic differential equations satisfying a global monotonicity condition is studied. The strong rate of convergence with respect to the mean square norm is determined to be \(\frac{1}{2}\) for the two-step BDF-Maruyama scheme and for the backward Euler–Maruyama method. In particular, this is the first paper which proves a strong convergence rate for a multi-step method applied to equations with possibly superlinearly growing drift and diffusion coefficient functions. We also present numerical experiments for the \(\tfrac{3}{2}\)-volatility model from finance and a two dimensional problem related to Galerkin approximation of SPDE, which verify our results in practice and indicate that the BDF2-Maruyama method offers advantages over Euler-type methods if the stochastic differential equation is stiff or driven by a noise with small intensity.

Vorheriger Artikel Superconvergent Nyström method for Urysohn integral equations

Nächster Artikel Practical splitting methods for the adaptive integration of nonlinear evolution equations. Part I: Construction of optimized schemes and pairs of schemes

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Titel: Mean-square convergence of the BDF2-Maruyama and backward Euler schemes for SDE satisfying a global monotonicity condition
verfasst von: Adam Andersson
Raphael Kruse
Publikationsdatum: 09.07.2016
Verlag: Springer Netherlands
Erschienen in: BIT Numerical Mathematics / Ausgabe 1/2017
Print ISSN: 0006-3835
Elektronische ISSN: 1572-9125
DOI: https://doi.org/10.1007/s10543-016-0624-y

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