Brownian sine terminal martingale
= Brownian sine terminal martingale
{title2=$\sin B_T=\int_0^T e^{-(T-s)/2}\cos B_s\,dB_s$}
The <conditional expectation> of $\sin B_T$ at time $t$ is $e^{-(T-t)/2}\sin B_t$, by independent <Brownian increment>. <Itô's formula> cancels its time derivative against its second spatial derivative and leaves the displayed <stochastic integral>. The integrand is bounded, so <Itô isometry> verifies its square integrability.