Electronic Communications in Probability
- Electron. Commun. Probab.
- Volume 22 (2017), paper no. 39, 9 pp.
A functional limit theorem for excited random walks
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.
Electron. Commun. Probab., Volume 22 (2017), paper no. 39, 9 pp.
Received: 11 November 2016
Accepted: 14 June 2017
First available in Project Euclid: 9 August 2017
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43] 60K37: Processes in random environments 60F17: Functional limit theorems; invariance principles
Pilipenko, Andrey. A functional limit theorem for excited random walks. Electron. Commun. Probab. 22 (2017), paper no. 39, 9 pp. doi:10.1214/17-ECP66. https://projecteuclid.org/euclid.ecp/1502244193