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Math Help - Estimate for an expectation

  1. #1
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    Estimate for an expectation

    Hello,

    I have the following situation: Two stochastic processes X and Y. For X, I know that E[|X_s]^2]\leq C for all s\in[t,T]. Now I need an estimate for the expression: E[|X_sY_s|^2, aim is to get rid of the X. Something like E[|X_sY_s|^2]\leq E[|X_s|^2]E[|Y_s|^2] (does this hold???). Then I would obtain E[|X_sY_s|^2]\leq C E[|Y_s|^2]. Then I would be happy.

    I hope, somebody has an idea.
    Thanks in adavance,
    twingeling
    Last edited by Moo; June 12th 2011 at 12:32 AM. Reason: putting the Tex tags
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  2. #2
    Moo
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    Hello,

    Can't you just use Cauchy-Schwarz inequality ?
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