Limits of bifractional Brownian noises
Abstract
Let $B^{H,K}=(B^{H,K}_{t}, t\geq 0)$ be a bifractional Brownian motion with two parameters $H\in (0,1)$ and $K\in(0,1]$. The main result of this paper is that the increment process generated by the bifractional Brownian motion $(B^{H,K}_{h+t} -B^{H,K}_{h}, t\geq 0)$ converges when $h\to \infty$ to $(2^{(1-K)/{2}}B^{HK}_{t}, t\geq 0)$, where $(B^{HK}_{t}, t\geq 0)$ is the fractional Brownian motion with Hurst index $HK$. We also study the behavior of the noise associated to the bifractional Brownian motion and limit theorems to $B^{H,K}$.
- Publication:
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arXiv e-prints
- Pub Date:
- October 2008
- DOI:
- 10.48550/arXiv.0810.4764
- arXiv:
- arXiv:0810.4764
- Bibcode:
- 2008arXiv0810.4764M
- Keywords:
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- Mathematics - Probability