Expected Value of product of Ito's Integral Any idea on how to compute the expected value of product of Ito's Integral with two different upper limit?
For example:
$$\mathbb{E}\left[\int_0^r f(t)\,dB(t) \int_0^s f(t)\,dB(t)\right]$$
I only know how to compute when the upper limit r and s are the same...but don't know how when r and s are different...help. 

Let $g(t)=f(t)\mathbf 1_{[0,r]}(t)$ and $h(t)=f(t)\mathbf 1_{[0,s]}(t)$ then $$\int_0^r f(t)\,\mathrm dB(t)=\int_0^\infty g(t)\,\mathrm dB(t),\qquad \int_0^r f(t)\,\mathrm dB(t)= \int_0^\infty h(t)\,\mathrm dB(t)$$ hence $$\mathbb{E}\left[\int_0^r f(t)\,\mathrm dB(t)\cdot \int_0^s f(t)\,\mathrm dB(t)\right]=\int_0^\infty g(t)h(t)\mathrm dt=\int_0^{\min(r,s)}f^2(t)\mathrm dt.$$
