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Discrete approximation of stochastic differential equations. (English) Zbl 1242.65011

Summary: It is shown how stochastic Itô-Taylor schemes for stochastic ordinary differential equations can be embedded into standard concepts of consistency, stability and convergence. An appropriate choice of function spaces and norms, in particular a stochastic generalization of Spijker’s norm (1968), leads to two-sided estimates for the strong error of convergence under the usual assumptions.

MSC:

65C30 Numerical solutions to stochastic differential and integral equations
60H30 Applications of stochastic analysis (to PDEs, etc.)
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