Stochastic integral ($\int HdX$)

The stochastic integral $\int HdX$ integrates a predictable process against a semimartingale. It extends pathwise integration against finite-variation processes and the Itô integral against local martingales.

Whenever the integrands are admissible,

For a square-integrable predictable process $H$ and Brownian motion $W$,

For a continuous local martingale $M$,