  We consider the limit behavior of an excited random walk (ERW), i.e., a
random walk whose transition probabilities depend on the number of times the
walk has visited to the current state. We prove that an ERW being naturally
scaled converges in distribution to an excited Brownian motion that satisfies
an SDE, where the drift of the unknown process depends on its local time.
Similar result was obtained by Raimond and Schapira, their proof was based on
the Ray-Knight type theorems. We propose a new method of investigations based
on a study of the Radon-Nikodym density of the ERW distribution with respect to
the distribution of a symmetric random walk.
