NDLI: Towards a Systematic Linear Stability Analysis of Numerical Methods for Systems of Stochastic Differential Equations

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Buckwar, Evelyn Kelly, Cnall
Copyright Year	2010
Abstract	We develop two classes of test equations for the linear stability analysis of numerical methods applied to systems of stochastic ordinary differential equations of It type (SODEs). Motivated by the theory of stochastic stabilization and destabilization, these test equations capture certain fundamental effects of stochastic perturbation in systems of SODEs, while remaining amenable to analysis before and after discretization. We then carry out a linear stability analysis of the $\theta$-Maruyama method applied to these test equations, investigating mean-square and almost sure asymptotic stability of the test equilibria. We discuss the implications of our work for the notion of A-stability of the $\theta$-Maruyama method and use numerical simulation to suggest extensions of our results to test systems with nonnormal drift coefficients. (A corrected version of this paper has been appended to the originally posted pdf.)
Starting Page	298
Ending Page	321
Page Count	24
File Format	PDF
ISSN	00361429
DOI	10.1137/090771843
e-ISSN	10957170
Issue Number	1
Volume Number	48
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2010-04-02
Access Restriction	Subscribed
Subject Keyword	linear stability analysis systems of stochastic differential equations Stability and convergence of numerical methods theta method Models, numerical methods stabilization Stochastic ordinary differential equations Computational methods for stochastic equations destabilization
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Numerical Analysis Computational Mathematics

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