Abstract
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.
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supported by CRC 701’ Spectral Analysis and Topological Structures in Mathematics’.
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Kruse, R. Discrete approximation of stochastic differential equations. SeMA 51, 83–90 (2010). https://doi.org/10.1007/BF03322558
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DOI: https://doi.org/10.1007/BF03322558
Key words
- SODE
- stochastic differential equations
- Itô-Taylor schemes
- discrete approximation
- bistability
- two-sided error estimates
- stochastic Spijker norm