Asymptotic error for the Milstein scheme for SDEs driven by continuous semimartingales

Details Asymptotic error for the Milstein scheme for SDEs driven by continuous semimartingales Asymptotic error for the Milstein scheme for SDEs driven by continuous semimartingales

2006-02-21

arxiv.org/abs/math/0602465v1

Annals of Applied Probability 2005, Vol. 15, No. 4, 2706-2738

Mathematics

Probability

Published at http://dx.doi.org/10.1214/105051605000000520 in the Annals of Applied Probability (http://www.imstat.org/aap/) by

Scientific paper

10.1214/105051605000000520

A Milstein-type scheme was proposed to improve the rate of convergence of its approximation of the solution to a stochastic differential equation driven by a vector of continuous semimartingales. A necessary and sufficient condition was provided for this rate to be $1/n$ when the SDE is driven by a vector of continuous local martingales, or continuous semimartingales under an additional assumption on their finite variation part. The asymptotic behavior (weak convergence) of the normalized error processes was also studied.

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