  We consider one-dimensional excited random walks (ERWs) with periodic cookie
stacks in the recurrent regime. We prove functional limit theorems for these
walks which extend the previous results of D. Dolgopyat and E. Kosygina for
excited random walks with "boundedly many cookies per site." In particular, in
the non-boundary recurrent case the rescaled excited random walk converges in
the standard Skorokhod topology to a Brownian motion perturbed at its extrema
(BMPE). While BMPE is a natural limiting object for excited random walks with
boundedly many cookies per site, it is far from obvious why the same should be
true for our model which allows for infinitely many "cookies" at each site.
Moreover, a BMPE has two parameters $\alpha,\beta<1$ and the scaling limits in
this paper cover a larger variety of choices for $\alpha$ and $\beta$ than can
be obtained for ERWs with boundedly many cookies per site.
