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Math Help - Azouma inequality for martingales

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    Azouma inequality for martingales

    I have to apply Azouma inequality to a Doob martingale. To do this I have to prove that my Doob martingale has bounded increments.

    Wikipedia explains a tecnique which could be very useful to me in order to bound increments (see Doob martingale - Wikipedia, the free encyclopedia "McDiarmid's Inequality" paragraph),
    but I can't understand a passage: why if the function f has bounded increments, then the martingale B has bounded increments?

    Could someone help me to write down a proof?
    Last edited by qwertyuio; April 15th 2012 at 07:02 AM.
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