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 D 1 p — 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.
KeywordsBrownian Motion Probability Space Variable Formula Stochastic Integration Energy Identity
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