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Zbl 0982.60051
Higham, Desmond J.
Mean-square and asymptotic stability of the stochastic theta method. (English)
[J] SIAM J. Numer. Anal. 38, No.3, 753-769 (2000). ISSN 0036-1429; ISSN 1095-7170/e

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.
[Eckhard Platen (Broadway)]
MSC 2000:
*60H10 Stochastic ordinary differential equations
65C20 Models (numerical methods)
65L20 Stability of numerical methods for ODE

Keywords: asymptotic stability; mean-square stability; multiplicative noise; random sequence; theta method

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