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 p1 — 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.
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© 1997 Springer-Verlag Berlin Heidelberg
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Malliavin, P. (1997). Itô’s Theory of Stochastic Integration. In: Stochastic Analysis. Grundlehren der mathematischen Wissenschaften, vol 313. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15074-6_7
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DOI: https://doi.org/10.1007/978-3-642-15074-6_7
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-15073-9
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