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

2005/11/01 by Liqing Yan · 2 citations
Economics, Econometrics and Finance · Mathematics · Social Sciences · #Financial Risk and Volatility Modeling #Insurance, Mortality, Demography, Risk Management #Stochastic processes and financial applications #math.PR #msc:60F05 #msc:60H10 #msc:60H35 #msc:65C05 #msc:68U20

paper · pdf · doi:10.1214/105051605000000520

published as Annals of Applied Probability 2005, Vol. 15, No. 4, 2706-2738 · Published at http://dx.doi.org/10.1214/105051605000000520 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)

openalex publication_date 2005/11/01 · arxiv created 2006/02/21 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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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