I am looking at the following expectation:
$\mathbb{E}[\int_{0}^{s}G(s')dW(s')\int_{s}^{t}H(t')dW(t')]$
Intuitively I think the expectation should be zero since the domain of the two integrals do not overlap. However, I am not sure how to show this. I was thinking I could rewrite the integral as a sum and then find the result, but I seem to get lost in the algebra. Any ideas?