Anthony Réveillac (INSA Toulouse)
Prof. Dr. Andrey Pilipenko (Kyiv)
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 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 based on a study of the
Radon-Nikodym density of the ERW distribution with respect to the distribution of
a symmetric random walk.