Invariance principles for Markov Cookie random walks
Thomas Mountford, EPFL, Switzerland
We take as starting point the recent work of Kosygina and Peterson (who are coworkers in the current project) and consider Markov cookie random walks in one dimension where the cookies at each site are generated by a Markov process. In the mean zero, recurrent case we show that the walk converges to a Brownian motion perturbed at extrema. The method is a coarse grained application of Ray Knight techniques.