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Let $x(t)$ a real valued stochastic process and $T>0$ a constant. Is it true that:

$$\mathbb{E}\left[\sup_{t\in [0,T]} |x(t)|\right] \leq T \sup_{t\in [0,T]} \mathbb{E}\left[|x(t)|\right] \text{ ?}$$

Thanks for your help.

  • 0
    Something smells fishy here. The LHS is scale-invariant, but the RHS is not, so we can rescale everything so that the RHS is arbitrarily small...2011-09-28

2 Answers 2