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Ito's formulaI have a book written by Shreve "Stochastic calculus for finance" and when he states the Ito's formula for the function he says that the derivatives should be continuous. But it's not enough to guarantee that the stochastic integral in the formula is actually an Ito's integral because there is no square-integrabilty assumption on . Also, when he discusses Feynman-Kac formula he doesn't make the assumption that is square-integrable but at the same time claims that the stochastic integral is a martingale. Why is that? |

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