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Math Help - Expectation and supremum

  1. #1
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    Expectation and supremum

    If [IMG]file:///C:/DOCUME%7E1/ADMINI%7E1/LOCALS%7E1/Temp/msohtml1/01/clip_image002.gif[/IMG][IMG]file:///C:/DOCUME%7E1/ADMINI%7E1/LOCALS%7E1/Temp/msohtml1/01/clip_image002.gif[/IMG][IMG]file:///C:/DOCUME%7E1/ADMINI%7E1/LOCALS%7E1/Temp/msohtml1/01/clip_image002.gif[/IMG]B_{t} is a Brownian motion starting from x and f is a function on R which is bounded above, is this inequality true?

    E[sup_{t}f(B_{t})]≤sup_{t}E[f(B_{t})]

    thanks[IMG]file:///C:/DOCUME%7E1/ADMINI%7E1/LOCALS%7E1/Temp/msohtml1/01/clip_image002.gif[/IMG]
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  2. #2
    Junior Member
    Joined
    Jun 2010
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    I believe you wanted in-text images. For me, they appear as meaningless text. As for Brownian motion, I haven't studied it, though I know some real analysis, so maybe I could figure it out. Could you attach the pictures?
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