A class of nonlinear random walks related to the Ornstein-Uhlenbeck process
Mathematical Physics
2011-10-31 v1 math.MP
Probability
Abstract
Contrary to the theory of Markov processes, no general theory exists for the so called nonlinear Markov processes. We study an example of "nonlinear Markov process" related to classical probability theory, merely to random walks. This model provides interesting phenomena (absent in classical Markov chains): continuum of stationary measures, conserved quantities, convergence to stationary classical random walks etc.
Keywords
Cite
@article{arxiv.1107.0850,
title = {A class of nonlinear random walks related to the Ornstein-Uhlenbeck process},
author = {S. A. Muzychka and K. L. Vaninsky},
journal= {arXiv preprint arXiv:1107.0850},
year = {2011}
}