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\(T\)-stability of numerical scheme for stochastic differential equations. (English) Zbl 0834.65146

Agarwal, R. P. (ed.), Contributions in numerical mathematics. Singapore: World Scientific Publishing Co. World Sci. Ser. Appl. Anal. Vol. 2, 333-344 (1993).
Summary: Stochastic differential equations (SDEs) represent physical phenomena dominated by stochastic processes. Like for deterministic differential equations, various numerical schemes are proposed for SDEs. Recently we investigated the stability notion of a numerical solution for SDEs. In this note we propose a new stability, \(T\)-stability, of numerical schemes for a scalar multiplicative SDE with respect to its pathwise approximation. When the two- or three-point random variables are chosen as the driving Wiener process, we examine \(T\)-stability of the Euler- Maruyama scheme together with numerical results.
For the entire collection see [Zbl 0829.00032].

MSC:

65C99 Probabilistic methods, stochastic differential equations
65L05 Numerical methods for initial value problems involving ordinary differential equations
65L20 Stability and convergence of numerical methods for ordinary differential equations
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
34F05 Ordinary differential equations and systems with randomness
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