Weak schemes, such as Ninomiya-Victoir or Ninomiya-Ninomiya, are typically used for discretization of stochastic volatility models such as the Heston Model.

Can anyone familiar with Cubature on Wiener Spaces explain why (i.e. with a detailed proof or a reference) these weak schemes can be seen as a Cubature scheme over Wiener Spaces?

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    $\begingroup$ You may try asking this question on mathoverflow.net, it seems to be math-heavy enough. $\endgroup$
    – quant_dev
    Feb 8, 2011 at 22:19
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    $\begingroup$ Well I 'm affraid that even this is "heavy math" the aim of the forum (in my opinion) is to address this kind of question. MO is more a "pure" math and don't want to pollute it with applicable themes such as Cubature methods in Finance. Regards $\endgroup$
    – TheBridge
    Feb 9, 2011 at 12:31
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    $\begingroup$ This is certainly on-topic here; it may just be that we don't have enough of an appropriate user-base yet. $\endgroup$
    – Shane
    Feb 14, 2011 at 14:50
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    $\begingroup$ @stonybrooknick : thank's that really helps. Why didn't I thought about that before ?? $\endgroup$
    – TheBridge
    Dec 9, 2011 at 11:16
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    $\begingroup$ @ vanguard2k : Yes it is, I think I know now what to prove but I am just too lazy to try to prove it. But if you are willing to do it, I would be delighted to read your attempt. As an indication about what is needed is to prove that moments of the Ninomiya-Victoir scheme matches the moments ot the stochastic iterative (stratanovitch)-integrals. Best regards $\endgroup$
    – TheBridge
    Oct 4, 2012 at 12:02


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