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What is the symbol that looks like a capital f, F, which is used to prove the martingale:

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    $\begingroup$ It's a capital $F$ in a calligraphic font. $\endgroup$ – Matthew Leingang Dec 13 '16 at 12:39
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    $\begingroup$ Without any context this is just a guess, but it might be a $\sigma$-field? $\endgroup$ – dinosaur Dec 13 '16 at 12:43
  • $\begingroup$ @dinosaur It was used to prove martingale $\endgroup$ – Betty Dec 13 '16 at 12:49
  • $\begingroup$ In general - filtration. In this particular - hard to say. $\endgroup$ – EzWin Dec 13 '16 at 12:53
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    $\begingroup$ $\mathcal{F}$ to produce $\mathcal{F}$ for a filtration $\endgroup$ – Henry Dec 13 '16 at 15:18
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My best guess is that $\mathcal{F}_s^B$ is a Brownian Filtration, with respective time $s$. See for instance Brownian Motion and Stochastic Calculus- section 2.7, from Karatzas and Shreve.

You can also see this notation being used here.

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