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Towards a systematic linear stability analysis of numerical methods for systems of stochastic differential equations. (English) Zbl 1221.60077
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.

60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
60H35 Computational methods for stochastic equations (aspects of stochastic analysis)
65C20 Probabilistic models, generic numerical methods in probability and statistics
65L20 Stability and convergence of numerical methods for ordinary differential equations
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