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Itô’s Theory of Stochastic Integration

  • Paul Malliavin
Part of the Grundlehren der mathematischen Wissenschaften book series (GL, volume 313)

Abstract

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.

Keywords

Brownian Motion Probability Space Variable Formula Stochastic Integration Energy Identity 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • Paul Malliavin

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