Limits of bifractional Brownian noises

International audienceLet $B^{H,K}=\left (B^{H,K}_{t}, t\geq 0\right )$ 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 $\left( B^{H,K}_{h+t} -B^{H,K} _{h}, t\geq 0\right)$ converges when $h\to \infty$ to $\left (2^{(1-K)/{2}}B^{HK} _{t}, t\geq 0\right )$, where $\left (B^{HK}_{t}, t\geq 0\right)$ 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 $B^{H,K}$