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

Mathematics – Probability

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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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