Mathematics – Probability
Scientific paper
2006-02-21
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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