An Inequality Related to Bifractional Brownian Motion

Mikhail Lifshits; Ilya Tyurin

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arXiv · 1105.4214

An Inequality Related to Bifractional Brownian Motion

Mikhail Lifshits·Ilya Tyurin

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Abstract

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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Mikhail Lifshits, Ilya Tyurin. 2011-05-21. An Inequality Related to Bifractional Brownian Motion. https://arxiv.org/abs/1105.4214

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