Berry-Esséen bounds and almost sure CLT for the quadratic variation of the bifractional Brownian motion

Details Berry-Esséen bounds and almost sure CLT for the quadratic variation of the bifractional Brownian motion Berry-Esséen bounds and almost sure CLT for the quadratic variation of the bifractional Brownian motion

2012-03-13

arxiv.org/abs/1203.2786v3

Mathematics

Probability

Scientific paper

Let $B$ be a bifractional Brownian motion with parameters $H\in (0, 1)$ and $K\in(0,1]$. For any $n\geq1$, set $Z_n =\sum_{i=0}^{n-1}\big[n^{2HK}(B_{(i+1)/n}-B_{i/n})^2-\E((B_{i+1}-B_{i})^2)\big]$. We use the Malliavin calculus and the so-called Stein's method on Wiener chaos introduced by Nourdin and Peccati \cite{NP09} to derive, in the case when $0

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