Recovery of a continuous Brownian integrand from short increments
= Recovery of a continuous Brownian integrand from short increments
For a bounded continuous <adapted process> $H$ and a <Brownian motion> $B$, $\int_t^{t+h}H_s\,dB_s/(B_{t+h}-B_t)$ converges in <probability> to $H_t$ as $h\downarrow0$. The <Itô isometry> makes the error numerator small relative to $\sqrt h$; the <normal distribution> of the denominator controls its chance of being too close to zero.