Itô’s Theory of Stochastic Integration

The probability space of Brownian motion and its filtration — Energy identity for stochastic integral of an adapted process — Itô’s stochastic integral of an adapted process — Chaos expansion in terms of iterated Itô stochastic integrals — Itô representation of a martingale by a stochastic integral — Clark-Bismut-Ocone representation of a martingale in D₁p — Itô calculus on semi-martingales — Covariance under C∞-maps of the Stratonovich representation of semi-martingales — Change of variables formula — Appendix: Estimates for Brownian martingales.