Pathwise Approximation of Random Ordinary Differential Equations

Titelangaben

Grüne, Lars ; Kloeden, Peter E.:
Pathwise Approximation of Random Ordinary Differential Equations.
In: BIT Numerical Mathematics. Bd. 41 (2001) Heft 4 . - S. 711-721.
ISSN 0006-3835
DOI: https://doi.org/10.1023/A:1021995918864

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Abstract

Standard error estimates for one-step numerical schemes for nonautonomous ordinary differential equations usually assume appropriate smoothness in both time and state variables and thus are not suitable for the pathwise approximation of random ordinary differential equations which are typically at most continuous or Hölder continuous in the time variable. Here it is shown that the usual higher order of convergence can be retained if one first averages the time dependence over each discretization subinterval.