Let $B=\{B^H(t)\}_{t\geq0}$ be a $d$-dimensional fractional Brownian motion with Hurst parameter $H\in (0,1)$. Consider the functionals of $k$ independent $d$-dimensional fractional Brownian motions $$ \frac{1}{\sqrt{n}} \int^{e^{nt_1}}_0\cdots\int^{e^{nt_k}}_0 f(B^{H,1}(s_1)+\cdots +B^{H,k}(s_k)){\rm d}s_1\cdots{\rm d}s_k, $$ where the Hurst index $H=k/d$. Using the method of moments, we prove the limit law and extending a result by Xu \cite{xu} of the case $k=1$. It can also be regarded as a fractional generalization of Biane \cite{biane} in the case of Brownian motion.
Qian YU
. A LIMIT LAW FOR FUNCTIONALS OF MULTIPLE INDEPENDENT FRACTIONAL BROWNIAN MOTIONS[J]. Acta mathematica scientia, Series B, 2020
, 40(3)
: 734
-754
.
DOI: 10.1007/s10473-020-0311-6
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