An extension of bifractional Brownian motion

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 $2HK=1$.