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Stochastic integration by parts to obtain Kailath Segall identity for iterated stochastic in...

The case $n=1$ is straighfoward. Now, applying Ito's formula and the definition of $\{I_n\}$ to integrate by parts we have: \begin{align*} I_n = \int_0^t I_{n-1} (s) \ d M_s = I_{n-1}M - \int_0^t I …
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