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On the stability of some second order numerical methods for weak approximation of Itô SDEs

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Abstract

In this paper, we first investigate the stability of two weak second order methods introduced by Debrabant and Rößler (Appl Numer Math 59:582–594, 2009) and Platen (Math Comput Simulation 38:69–76, 1995). We then propose a new weak second order predictor-corrector method, with an improved stability properties, based on the Rößler’s method as the predictor and the implicit method of Platen as the corrector. The stability functions of these methods, applied to a scalar linear test equation with multiplicative noise, are determined and their regions of stability are then compared with the corresponding stability regions of the test equation. Furthermore, we also investigate mean square stability (MS-stability) of these methods applied to a linear Itô 2-dimensional stochastic differential test equation. Numerical examples will be presented to support the theoretical results.

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Authors and Affiliations

  1. Department of Applied Mathematics, Faculty of Mathematical Sciences, Tarbiat Modares University, P.O. Box 14115-175, Tehran, Iran

    Amir Haghighi & S. Mohammad Hosseini

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  1. Amir Haghighi
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  2. S. Mohammad Hosseini
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Correspondence to S. Mohammad Hosseini.

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Haghighi, A., Hosseini, S.M. On the stability of some second order numerical methods for weak approximation of Itô SDEs. Numer Algor 57, 101–124 (2011). https://doi.org/10.1007/s11075-010-9417-6

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  • DOI: https://doi.org/10.1007/s11075-010-9417-6

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