# Estimate for an expectation

• June 9th 2011, 04:15 AM
twingeling
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.