Probability Surveys
- Probab. Surveys
- Volume 4 (2007), 1-79.
A survey of random processes with reinforcement
Abstract
The models surveyed include generalized Pólya urns, reinforced random walks, interacting urn models, and continuous reinforced processes. Emphasis is on methods and results, with sketches provided of some proofs. Applications are discussed in statistics, biology, economics and a number of other areas.
Article information
Source
Probab. Surveys, Volume 4 (2007), 1-79.
Dates
First available in Project Euclid: 23 February 2007
Permanent link to this document
https://projecteuclid.org/euclid.ps/1172244137
Digital Object Identifier
doi:10.1214/07-PS094
Mathematical Reviews number (MathSciNet)
MR2282181
Zentralblatt MATH identifier
1189.60138
Subjects
Primary: 60J20: Applications of Markov chains and discrete-time Markov processes on general state spaces (social mobility, learning theory, industrial processes, etc.) [See also 90B30, 91D10, 91D35, 91E40] 60G50: Sums of independent random variables; random walks
Secondary: 37A50: Relations with probability theory and stochastic processes [See also 60Fxx and 60G10]
Keywords
urn model urn scheme Pólya’s urn stochastic approximation dynamical system exchangeability Lyapunov function reinforced random walk ERRW VRRW learning agent-based model evolutionary game theory self-avoiding walk
Citation
Pemantle, Robin. A survey of random processes with reinforcement. Probab. Surveys 4 (2007), 1--79. doi:10.1214/07-PS094. https://projecteuclid.org/euclid.ps/1172244137
