Brownian martingale representation theorem
= Brownian martingale representation theorem
{c}
Every square-integrable random variable measurable with respect to a Brownian filtration can be written as its expectation plus an <Itô integral> against that Brownian motion. Equivalently, every square-integrable martingale in that filtration has the form
$$
M_t=M_0+\int_0^tH_s\,dW_s
$$
for a predictable square-integrable process $H$.