Article | REF: AF105 V1

Stochastic Differential Equations

Author: Thierry CHONAVEL

Publication date: April 10, 2015, Review date: July 8, 2015

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4. Digital EDS integration

We'll see that ODE integration methods can be adapted for the numerical calculation of EDS, but that in this case their order (i.e. their speed of convergence) is lower when applied to ODEs. We'll start by considering Eurler's method, comparing its behavior in the deterministic and stochastic cases. We'll then look at the Milstein method and the Runge-Kutta method, which are more sophisticated but preferable to it.

4.1 A reminder of EDO digital integration

To integrate EDOs of the form ddtxt=bt(xt)...

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Digital EDS integration