An Inequality Related to Bifractional Brownian Motion

Details An Inequality Related to Bifractional Brownian Motion An Inequality Related to Bifractional Brownian Motion

2011-05-21

arxiv.org/abs/1105.4214v1

Mathematics

Probability

5 pages

Scientific paper

We prove that for any pair of i.i.d. random variables $X,Y$ with finite
moment of order $a \in (0,2]$ it is true that $E |X-Y|^a \leq E |X+Y|^a$.
Surprisingly, this inequality turns out to be related with bifractional
Brownian motion. We extend this result to Bernstein functions and provide some
counter-examples.

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