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2017 A functional limit theorem for excited random walks
Andrey Pilipenko
Electron. Commun. Probab. 22: 1-9 (2017). DOI: 10.1214/17-ECP66


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 based on a study of the Radon-Nikodym density of the ERW distribution with respect to the distribution of a symmetric random walk.


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Andrey Pilipenko. "A functional limit theorem for excited random walks." Electron. Commun. Probab. 22 1 - 9, 2017.


Received: 11 November 2016; Accepted: 14 June 2017; Published: 2017
First available in Project Euclid: 9 August 2017

zbMATH: 06797792
MathSciNet: MR3685237
Digital Object Identifier: 10.1214/17-ECP66

Primary: 60F17, 60K35, 60K37


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