2011/05/21 by Mikhail Lifshits, Lifshits, Mikhail, Ilya Tyurin +1
Mathematics · #60E15 #60G22 #FOS: Mathematics #Probability (math.PR) #math.PR #msc:60E15 #msc:60G22
paper · pdf · doi:10.48550/arxiv.1105.4214
5 pages
arxiv created 2011/05/21 · arxiv updated 2011/05/24
We prove that for any pair of i.i.d. random variables X,Y with finite moment of order a ∈ (0,2] it is true that E |X-Y|a ≤ 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.