Square-integrable stochastic integrand ($L^2(M)$)

For a zero-starting L2-bounded continuous martingale $M$, the space $L^2(M)$ consists of predictable $H$ with $\mathbb{E}{\int }_0^{\infty }{H}_s^{2}d[M{]}_s<\infty$, identifying processes equal almost everywhere for the quadratic-variation measure. The finite-horizon version stops the integral at $T$. The Itô integral is the isometric extension from elementary predictable integrands.

// Target: probability-and-statistics.bigb