Convergence to the local time of Brownian meander

Let {S-n, n >= 0} be integer-valued random walk with zero drift and variance sigma(2). Let xi (k, n) be number of t is an element of {1, ..., n} such that S(t) = k. For the sequence of random processes xi( left perpendicular u sigma root n right perpendicular, n) considered under conditions S-1 > 0, ..., S-n > 0 a functional limit theorem on the convergence to the local time of Brownian meander is proved.