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In this post, Ofer says that taking the convex combination of two Girsanov measures yields a drift $BF_1+(1-B)F_2$ where $B$ is a Bernoulli random variable with parameter $\lambda$, independent of the underlying probability measure. I am a bit confused - where does the mixing occur? Why do we have to enlarge the space?

Since $\mu=\lambda\mu_1+(1-\lambda)\mu_2$ is a Girsanov measure there is a drift in the original space, you shouldn't have to enlarge it, right?

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  • $\begingroup$ Sorry, what do you mean precisely by mixing? $\endgroup$
    – Nate River
    Commented May 15, 2021 at 18:47
  • $\begingroup$ @NateRiver I just mean that we are "mixing" over $F_1$ and $F_2$ $\endgroup$
    – user207651
    Commented May 15, 2021 at 18:59

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