A Note on Transience of Generalized Multi-Dimensional Excited Random Walks

Abstract

We consider a variant 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 more slowly than \(n^{-\beta _0}\) (n is time), where \(\beta _0\) depends on the transitions of the process, the GERW is transient in the direction of the drift.