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



Numerical computation of Skorokhod integral
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})
$


