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Zbl 1221.60077
Buckwar, Evelyn; Kelly, Cónall
Towards a systematic linear stability analysis of numerical methods for systems of stochastic differential equations. (English)
[J] SIAM J. Numer. Anal. 48, No. 1, 298-321 (2010). ISSN 0036-1429; ISSN 1095-7170/e

Aiming for effectiveness while retaining acceptable simplicity, two classes of test systems are devised for investigating mean square stability and almost sure stability of numerical methods for solving systems of Itô stochastic differential equations. The use and advantages of these test systems are illustrated by analyzing the stability of the $\theta$-Maruyama method.
[Melvin D. Lax (Long Beach)]

MSC 2000:: *60H10 Stochastic ordinary differential equations
60H35 Computational methods for stochastic equations
65C20 Models (numerical methods)
65L20 Stability of numerical methods for ODE

Keywords: linear stability analysis; theta method; systems of stochastic differential equations; stabilization; destabilization

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Zentralblatt MATH Berlin [Germany]