# Malliavin Derivative with Mathematica is it possible? [closed]

Is it possible to define a Malliavin calculus with Mathematica 9?

Consider a random variables on the Wiener-space $\Omega=\mathcal{C}([0,1])$ of the form $$F=F(\omega)=\displaystyle\int_{0}^{T}h_{t}dW_{t}$$ for some deterministic $h(.)$ in $L^{2}[0,T].$ Here, $\omega$ is a path in the Wiener-space, $\omega \in \Omega$.

We define the Malliavin derivative by

$$DF=h,\text{ and }D_{t}F=h_{t}.$$ Let say MalliavinDer is this derivative. We have the following rules

1. MalliavinDer[F_ + G_] := MalliavinDer[F]+MalliavinDer[G];
2. MalliavinDer[F_G_]:=MalliavinDer[F]G+ MalliavinDer[G]F
3. MalliavinDer[f(F)]:=f'[F]MalliavinDer[F].

On the other hand, we have for example:

1. MalliavinDer[\int_0^T h(t)dWt] := h(t)
2. MalliavinDer[W_s] := Piecewise[{{1, s <t}, {0, s >t}}]
3. MalliavinDer[f(W_s] := f'[W_s])Piecewise[{{1, s <t}, {0, s >t}}]
• Hi Zbigniew, and welcome to scicomp. Unfortunately, we don't handle questions pertaining directly to Mathematica. These questions are more appropriately addressed in the Mathematica stack exchange website. – Paul Aug 8 '13 at 21:09