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How can I numerically compute the Skorokhod integral of a non-adapted process? If it is adapted, that is easy since the integral is just an Ito integral.

I have found that computing the Malliavin derivative is also easy using finite differences, by bumping the Brownian path at a time t. But I can't figure out how to achieve the inverse operation.

Thank you

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If you are looking for approximations of the Skorohod integral we can use Wick Riemann sums.

Define for $F \in \mathbb{D}^{1,2}$ and $W$ a Wiener process the Wick product $F \star W_t$ by

$F \star W_t=FW_t -\int_0^t D_s F ds$

then the Skorohod integral $\delta (u)$ of a possibly non-adapted process $u$ is the limit in $L^2$ of the forward Wick Riemann sums

$ \sum u_{t_i} \star (W_{t_{i+1}} -W_{t_i}) $

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  • $\begingroup$ Hi Fabrice, could you provide a reference for me to the Wick Riemann sums thing, I'd like to read more on it; thanks. $\endgroup$
    – ABIM
    Commented Oct 28, 2015 at 17:37
  • $\begingroup$ down.cenet.org.cn/upfile/36/20051120233229116.pdf $\endgroup$
    – ABIM
    Commented Nov 3, 2015 at 17:55

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