I am trying to compute the quadratic variation of $ \cos (B_t)$. Using Ito's formula I have deduced that we would get that the quadratic variation is given by: $$[\cos B](t) = \int^t_0 \sin^2(B_s)ds $$ but I can't reduce this problem any further as I can't compute this integral. Indeed I'm not even sure this is the right approach. Any hints would be welcome.

Thanks for the help.

  • $\begingroup$ Can you compute its expectation and variance? (I'm not very familiar with the topic, it just seems like a natural thing to do.) $\endgroup$ – Dap Oct 3 '17 at 9:24
  • $\begingroup$ thanks, as it turns out I think this is actually as far as the quadratic variation can be reduced $\endgroup$ – Flintro Oct 4 '17 at 13:06

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