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Mean-square and asymptotic stability of the stochastic theta method. (English) Zbl 0982.60051
The paper studies a linear test equation with multiplicative noise and considers mean-square and asymptotic numerical stability. An extension of the deterministic A-stability is shown to hold. Mean-square stability regions are visualized.

MSC:
60H10 Stochastic ordinary differential 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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