Let $M_t$ be a continuous local martingale with $M_0=0$ and define $I_t^0=1$ and $I_t^n= \int_0^t I_s^{n-1}\; dM_s$. Prove that we have $n I_t^n= I_t^{n-1}- \int_0^t I_s^{n-2} \;d((M)_t) $ where $(M)_t$ is the quadratic variation of $M$.
An identity about a continuous local martingale
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probability-theory
stochastic-processes
martingales
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1@phil Could you tell us where you found this formula? – 2011-12-02