# Thread:

1. ## 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

2. Hello,

Can't you just use Cauchy-Schwarz inequality ?
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