A note on transience of generalized many-dimensional excited random walks

We consider a variation of the Generalized Excited Random Walk (GERW) in dimension $d\ge 2$ where the lower bound on the drift for excited jumps is time-dependent and decays to zero. We show that if the lower bound decays slower that $n^{-\beta }$ ($n$ is time), for $\beta$ depending on the transitions of the process, the GERW is transient in the direction of the drift.