Abstract

The probability space of Brownian motion and its filtration — Energy identity for stochastic integral of an adapted process — Ito’s stochastic integral of an adapted process — Chaos expansion in terms of iterated Ito stochastic integrals — Ito representation of a martingale by a stochastic integral — Clark-Bismut-Ocone representation of a martingale in D 1 p — Ito calculus on semi-martingales — Covariance under C∞-maps of the Stratonovich representation of semi-martingales — Change of variables formula — Appendix: Estimates for Brownian martingales.

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