Bifractional Brownian motion for $H>1$ and $2HK\le 1$.

Bifractional Brownian motion on $\mathbb{R}_+$ is a two parameter centered Gaussian process with covariance function: $$ R_{H,K} (t,s)=\frac 1{2^K}\left(\left(t^{2H}+s^{2H}\right)^K-\vert t-s\vert^{2HK}\right), \qquad s,t\ge 0. $$ This process has been originally introduced by Houdr\'e and Villa (2002) for the range of parameters $H\in (0,1]$ and $K\in (0,1]$. Since then, the range of parameters, for which $R_{H,K}$ is known to be nonnegative definite has been somewhat extended, but the full range is still not known. In the present paper we give an elementary proof that $R_{H,K}$ is nonnegative definite for parameters $H,K$ satisfying $H>1$ and $0 1$.