Hi there,
I want to calculate:
\mathbb{E}(J_{1}* J_{10}* J_{10 }*J_{110})
where
J_{1}=\int 1 dW,
J_{10}=\int\int 1 dW dt,
J_{110= }\int \int \int 1 dW dW dt
are multiple Stratonovich Integrals over the interval [t_{0},T], h:=T-t_{0}, W is Brownian motion/ Wiener process (same notation like Kloeden and Platen use in Numerical Solution of SDEs).
J_{1}*J_{110}=3*J_{1110}+J_{1101} (Preposition 5.2.10 in kloeden and Platen), but that leaves me with:
\mathbb{E}(J_{10}* J_{10 }*(3*J_{1110}+J_{1101})).
I know how to change the stratonovich integrals into Ito integrals. And I know how to calculate the expected value of the product of 2 Ito integrals. But how can I calculate the expected value of the product of more than 2 ito Integrals? Or do you have another idea about calculating the expected value of \mathbb{E}(J_{10}* J_{10 }*(3*J_{1110}+J_{1101}))?
Thak you sooooooo much.