  In this paper we introduce and study a self-similar Gaussian process that is
the bifractional Brownian motion $B^{H,K}$ with parameters $H\in (0,1)$ and
$K\in(1,2)$ such that $HK\in(0,1)$. A remarkable difference between the case
$K\in(0,1)$ and our situation is that this process is a semimartingale when
$2HK=1$.

Probability