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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 θ-Maruyama method.
MSC:
60H10Stochastic ordinary differential equations
60H35Computational methods for stochastic equations
65C20Models (numerical methods)
65L20Stability and convergence of numerical methods for ODE