Let (F, G) be smooth, bounded cylindrical functions. Show that a) (D_{t}(F G)=G D_{t} F+F D_{t} G).

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Let $F, G$ be smooth, bounded cylindrical functions. Show that

a) $D_{t}(F G)=G D_{t} F+F D_{t} G$.

b) $D_{t}^{m}(F G)=\sum_{k=0}^{m}\left(\begin{array}{c}m \\ k\end{array}ight) D_{t}^{k} F \cdot D_{t}^{m-k} G$.

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Brownian Motion A Guide To Random Processes And Stochastic Calculus De Gruyter Textbook

ISBN: 9783110741254

3rd Edition

Authors: René L. Schilling, Björn Böttcher

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Question Posted: Mar 17, 2024 01:00 AM

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Let (F, G) be smooth, bounded cylindrical functions. Show that a) (D_{t}(F G)=G D_{t} F+F D_{t} G).

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Brownian Motion A Guide To Random Processes And Stochastic Calculus De Gruyter Textbook

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